/** @tests java.math.BigInteger#divideAndRemainder(java.math.BigInteger) */
@TestTargetNew(
level = TestLevel.PARTIAL,
notes = "ArithmeticException checked",
method = "divideAndRemainder",
args = {java.math.BigInteger.class})
public void test_divideAndRemainderLjava_math_BigInteger() {
try {
largePos.divideAndRemainder(zero);
fail("ArithmeticException expected");
} catch (ArithmeticException e) {
}
try {
bi1.divideAndRemainder(zero);
fail("ArithmeticException expected");
} catch (ArithmeticException e) {
}
try {
bi3.negate().divideAndRemainder(zero);
fail("ArithmeticException expected");
} catch (ArithmeticException e) {
}
try {
zero.divideAndRemainder(zero);
fail("ArithmeticException expected");
} catch (ArithmeticException e) {
}
}
public static void divideAndRemainder(int order) {
int failCount1 = 0;
for (int i = 0; i < size; i++) {
BigInteger x = fetchNumber(order).abs();
while (x.compareTo(BigInteger.valueOf(3L)) != 1) x = fetchNumber(order).abs();
BigInteger z = x.divide(BigInteger.valueOf(2L));
BigInteger y[] = x.divideAndRemainder(x);
if (!y[0].equals(BigInteger.ONE)) {
failCount1++;
System.err.println("fail1 x :" + x);
System.err.println(" y :" + y);
} else if (!y[1].equals(BigInteger.ZERO)) {
failCount1++;
System.err.println("fail2 x :" + x);
System.err.println(" y :" + y);
}
y = x.divideAndRemainder(z);
if (!y[0].equals(BigInteger.valueOf(2))) {
failCount1++;
System.err.println("fail3 x :" + x);
System.err.println(" y :" + y);
}
}
report("divideAndRemainder for " + order + " bits", failCount1);
}
public static void main(String[] args) throws NumberFormatException, IOException {
BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
int t = Integer.parseInt(br.readLine());
long n;
BigInteger sum;
BigInteger[] res;
for (int i = 0; i < t; i++) {
br.readLine();
n = Integer.parseInt(br.readLine());
if (n == 0) {
System.out.println("YES");
continue;
}
sum = new BigInteger("0");
for (int j = 0; j < n; j++) {
sum = sum.add(new BigInteger(br.readLine()));
}
res = sum.divideAndRemainder(new BigInteger(n + ""));
if (res[1].toString().equals("0")) {
System.out.println("YES");
} else {
System.out.println("NO");
}
}
}
public static void arithmetic(int order) {
int failCount = 0;
for (int i = 0; i < size; i++) {
BigInteger x = fetchNumber(order);
while (x.compareTo(BigInteger.ZERO) != 1) x = fetchNumber(order);
BigInteger y = fetchNumber(order / 2);
while (x.compareTo(y) == -1) y = fetchNumber(order / 2);
if (y.equals(BigInteger.ZERO)) y = y.add(BigInteger.ONE);
BigInteger baz = x.divide(y);
baz = baz.multiply(y);
baz = baz.add(x.remainder(y));
baz = baz.subtract(x);
if (!baz.equals(BigInteger.ZERO)) failCount++;
}
report("Arithmetic I for " + order + " bits", failCount);
failCount = 0;
for (int i = 0; i < 100; i++) {
BigInteger x = fetchNumber(order);
while (x.compareTo(BigInteger.ZERO) != 1) x = fetchNumber(order);
BigInteger y = fetchNumber(order / 2);
while (x.compareTo(y) == -1) y = fetchNumber(order / 2);
if (y.equals(BigInteger.ZERO)) y = y.add(BigInteger.ONE);
BigInteger baz[] = x.divideAndRemainder(y);
baz[0] = baz[0].multiply(y);
baz[0] = baz[0].add(baz[1]);
baz[0] = baz[0].subtract(x);
if (!baz[0].equals(BigInteger.ZERO)) failCount++;
}
report("Arithmetic II for " + order + " bits", failCount);
}
public static void shift(int order) {
int failCount1 = 0;
int failCount2 = 0;
int failCount3 = 0;
for (int i = 0; i < 100; i++) {
BigInteger x = fetchNumber(order);
int n = Math.abs(rnd.nextInt() % 200);
if (!x.shiftLeft(n).equals(x.multiply(BigInteger.valueOf(2L).pow(n)))) failCount1++;
BigInteger y[] = x.divideAndRemainder(BigInteger.valueOf(2L).pow(n));
BigInteger z = (x.signum() < 0 && y[1].signum() != 0 ? y[0].subtract(BigInteger.ONE) : y[0]);
BigInteger b = x.shiftRight(n);
if (!b.equals(z)) {
System.err.println("Input is " + x.toString(2));
System.err.println("shift is " + n);
System.err.println("Divided " + z.toString(2));
System.err.println("Shifted is " + b.toString(2));
if (b.toString().equals(z.toString())) System.err.println("Houston, we have a problem.");
failCount2++;
}
if (!x.shiftLeft(n).shiftRight(n).equals(x)) failCount3++;
}
report("baz shiftLeft", failCount1);
report("baz shiftRight", failCount2);
report("baz shiftLeft/Right", failCount3);
}
private void testDiv(BigInteger i1, BigInteger i2) {
BigInteger q = i1.divide(i2);
BigInteger r = i1.remainder(i2);
BigInteger[] temp = i1.divideAndRemainder(i2);
assertTrue("divide and divideAndRemainder do not agree", q.equals(temp[0]));
assertTrue("remainder and divideAndRemainder do not agree", r.equals(temp[1]));
assertTrue(
"signum and equals(zero) do not agree on quotient", q.signum() != 0 || q.equals(zero));
assertTrue(
"signum and equals(zero) do not agree on remainder", r.signum() != 0 || r.equals(zero));
assertTrue(
"wrong sign on quotient", q.signum() == 0 || q.signum() == i1.signum() * i2.signum());
assertTrue("wrong sign on remainder", r.signum() == 0 || r.signum() == i1.signum());
assertTrue("remainder out of range", r.abs().compareTo(i2.abs()) < 0);
assertTrue("quotient too small", q.abs().add(one).multiply(i2.abs()).compareTo(i1.abs()) > 0);
assertTrue("quotient too large", q.abs().multiply(i2.abs()).compareTo(i1.abs()) <= 0);
BigInteger p = q.multiply(i2);
BigInteger a = p.add(r);
assertTrue("(a/b)*b+(a%b) != a", a.equals(i1));
try {
BigInteger mod = i1.mod(i2);
assertTrue("mod is negative", mod.signum() >= 0);
assertTrue("mod out of range", mod.abs().compareTo(i2.abs()) < 0);
assertTrue("positive remainder == mod", r.signum() < 0 || r.equals(mod));
assertTrue(
"negative remainder == mod - divisor", r.signum() >= 0 || r.equals(mod.subtract(i2)));
} catch (ArithmeticException e) {
assertTrue("mod fails on negative divisor only", i2.signum() <= 0);
}
}
/**
* Returns a BigDecimal representation of this fraction. If possible, the returned value will be
* exactly equal to the fraction. If not, the BigDecimal will have a scale large enough to hold
* the same number of significant figures as both numerator and denominator, or the equivalent of
* a double-precision number, whichever is more.
*/
public BigDecimal toBigDecimal() {
// Implementation note: A fraction can be represented exactly in base-10 iff its
// denominator is of the form 2^a * 5^b, where a and b are nonnegative integers.
// (In other words, if there are no prime factors of the denominator except for
// 2 and 5, or if the denominator is 1). So to determine if this denominator is
// of this form, continually divide by 2 to get the number of 2's, and then
// continually divide by 5 to get the number of 5's. Afterward, if the denominator
// is 1 then there are no other prime factors.
// Note: number of 2's is given by the number of trailing 0 bits in the number
int twos = denominator.getLowestSetBit();
BigInteger tmpDen = denominator.shiftRight(twos); // x / 2^n === x >> n
final BigInteger FIVE = BigInteger.valueOf(5);
int fives = 0;
BigInteger[] divMod = null;
// while(tmpDen % 5 == 0) { fives++; tmpDen /= 5; }
while (BigInteger.ZERO.equals((divMod = tmpDen.divideAndRemainder(FIVE))[1])) {
fives++;
tmpDen = divMod[0];
}
if (BigInteger.ONE.equals(tmpDen)) {
// This fraction will terminate in base 10, so it can be represented exactly as
// a BigDecimal. We would now like to make the fraction of the form
// unscaled / 10^scale. We know that 2^x * 5^x = 10^x, and our denominator is
// in the form 2^twos * 5^fives. So use max(twos, fives) as the scale, and
// multiply the numerator and deminator by the appropriate number of 2's or 5's
// such that the denominator is of the form 2^scale * 5^scale. (Of course, we
// only have to actually multiply the numerator, since all we need for the
// BigDecimal constructor is the scale.
BigInteger unscaled = numerator;
int scale = Math.max(twos, fives);
if (twos < fives) unscaled = unscaled.shiftLeft(fives - twos); // x * 2^n === x << n
else if (fives < twos) unscaled = unscaled.multiply(FIVE.pow(twos - fives));
return new BigDecimal(unscaled, scale);
}
// else: this number will repeat infinitely in base-10. So try to figure out
// a good number of significant digits. Start with the number of digits required
// to represent the numerator and denominator in base-10, which is given by
// bitLength / log[2](10). (bitLenth is the number of digits in base-2).
final double LG10 = 3.321928094887362; // Precomputed ln(10)/ln(2), a.k.a. log[2](10)
int precision = Math.max(numerator.bitLength(), denominator.bitLength());
precision = (int) Math.ceil(precision / LG10);
// If the precision is less than 18 digits, use 18 digits so that the number
// will be at least as accurate as a cast to a double. For example, with
// the fraction 1/3, precision will be 1, giving a result of 0.3. This is
// quite a bit different from what a user would expect.
if (precision < 18) precision = 18;
return toBigDecimal(precision);
}
static int[] convertToCodewords(BigInteger binary) {
int[] codewords = new int[10];
BigInteger[] quotRem;
quotRem = binary.divideAndRemainder(BigInteger.valueOf(636));
codewords[9] = quotRem[1].intValue();
binary = quotRem[0];
final BigInteger const1365 = BigInteger.valueOf(1365);
for (int i = 8; i >= 1; i--) {
quotRem = binary.divideAndRemainder(const1365);
codewords[i] = quotRem[1].intValue();
binary = quotRem[0];
}
codewords[0] = binary.intValue();
return codewords;
}
public static BigInteger reverse(BigInteger in) {
BigInteger out = BigInteger.ZERO;
while (in.compareTo(BigInteger.ZERO) != 0) {
BigInteger tmp[] = in.divideAndRemainder(BigInteger.TEN);
out = out.multiply(BigInteger.TEN).add(tmp[1]);
in = tmp[0];
}
// System.gc();
return out;
}
/**
* Convert the specified giant value to a string with the specified radix.
*
* @param value The value to be converted.
* @param radix The radix.
* @return Returns a string representation in the specified radix.
*/
public static String convert(BigInteger value, int radix) {
BigInteger bigRadix = BigInteger.valueOf(radix);
StringBuilder sb = new StringBuilder();
while (value.compareTo(BigInteger.ZERO) > 0) {
BigInteger[] result = value.divideAndRemainder(bigRadix);
sb.append(radixChars[result[1].intValue()]);
value = result[0];
}
sb.reverse();
return sb.toString();
}
@Override
public void validate(FacesContext context, UIComponent component, Object value)
throws ValidatorException {
if (value instanceof String) {
String enteredOgrn = ((String) value).replaceAll("_+$", "");
Matcher matcher = OGRN_OGRNIP_REGEX.matcher(enteredOgrn);
if (!matcher.matches()) {
FacesMessage message = new FacesMessage();
message.setDetail(ERROR_MESSAGE);
message.setSummary(ERROR_MESSAGE);
message.setSeverity(FacesMessage.SEVERITY_ERROR);
context.addMessage(component.getClientId(), message);
throw new ValidatorException(message);
} else {
boolean correct = true;
int length;
BigInteger divisor;
if (enteredOgrn.length() == OGRN_LENGTH) {
length = OGRN_LENGTH;
divisor = OGRN_DIVISOR;
} else {
length = OGRNIP_LENGTH;
divisor = OGRNIP_DIVISOR;
}
int last = Character.getNumericValue(enteredOgrn.charAt(length - 1));
BigInteger ogrn = new BigInteger(enteredOgrn.substring(0, length - 1));
BigInteger[] divisionResult = ogrn.divideAndRemainder(divisor);
int remainder = divisionResult[1].intValue();
if (remainder > REMAINDER_THRESHOLD) {
remainder = remainder % 10;
}
if (remainder != last) {
correct = false;
}
if (!correct) {
FacesMessage message = new FacesMessage();
message.setDetail(INCORRECT_BY_CHECK_DIGIT);
message.setSummary(INCORRECT_BY_CHECK_DIGIT);
message.setSeverity(FacesMessage.SEVERITY_ERROR);
context.addMessage(component.getClientId(), message);
throw new ValidatorException(message);
}
}
} else {
FacesMessage message = new FacesMessage();
message.setDetail(ERROR_MESSAGE);
message.setSummary(ERROR_MESSAGE);
message.setSeverity(FacesMessage.SEVERITY_ERROR);
context.addMessage(component.getClientId(), message);
throw new ValidatorException(message);
}
}
/** Constructs a new BigFraction from the given BigDecimal object. */
private static BigFraction valueOfHelper(final BigDecimal d) {
// BigDecimal format: unscaled / 10^scale.
BigInteger tmpNumerator = d.unscaledValue();
BigInteger tmpDenominator = BigInteger.ONE;
// Special case for d == 0 (math below won't work right)
// Note: Cannot use d.equals(BigDecimal.ZERO), because
// BigDecimal.equals()
// does not consider numbers equal if they have different scales. So,
// 0.00 is not equal to BigDecimal.ZERO.
if (tmpNumerator.equals(BigInteger.ZERO)) {
return BigFraction.ZERO;
}
if (d.scale() < 0) {
tmpNumerator = tmpNumerator.multiply(BigInteger.TEN.pow(-d.scale()));
} else if (d.scale() > 0) {
// Now we have the form: unscaled / 10^scale = unscaled / (2^scale *
// 5^scale)
// We know then that gcd(unscaled, 2^scale * 5^scale) = 2^commonTwos
// * 5^commonFives
// Easy to determine commonTwos
final int commonTwos = Math.min(d.scale(), tmpNumerator.getLowestSetBit());
tmpNumerator = tmpNumerator.shiftRight(commonTwos);
tmpDenominator = tmpDenominator.shiftLeft(d.scale() - commonTwos);
// Determining commonFives is a little trickier..
int commonFives = 0;
BigInteger[] divMod = null;
// while(commonFives < d.scale() && tmpNumerator % 5 == 0) {
// tmpNumerator /= 5; commonFives++; }
while (commonFives < d.scale()
&& BigInteger.ZERO.equals((divMod = tmpNumerator.divideAndRemainder(BIGINT_FIVE))[1])) {
tmpNumerator = divMod[0];
commonFives++;
}
if (commonFives < d.scale()) {
tmpDenominator = tmpDenominator.multiply(BIGINT_FIVE.pow(d.scale() - commonFives));
}
}
// else: d.scale() == 0: do nothing
// Guaranteed there is no gcd, so fraction is in lowest terms
return new BigFraction(tmpNumerator, tmpDenominator, Reduced.YES);
}
/**
* @param Var varQuotient: destination variable that will receive the quotient of the last divide
* operation, recomputed as an integer divide
* @param Var varRest: destination variable that will receive the rest of the last divide
* operation, recomputed as an integer divide
* @return The last division is done again, as an integer one. This to method must follow
* immediatly the division to do.
*/
public MathDivide to(VarAndEdit varQuotient, VarAndEdit varRest) {
if (m_dA != null && m_dB != null) {
// Do the integer division
BigInteger nA = m_dA.toBigInteger();
BigInteger nB = m_dB.toBigInteger();
BigInteger[] t = nA.divideAndRemainder(nB);
int n = t[0].intValue();
varQuotient.set(n);
if (varRest != null) {
n = t[1].intValue();
varRest.set(n);
}
}
return this;
}
public void EX()
throws IrregularStringOfBitsException, IntegerOverflowException, TwosComplementSumException,
DivisionByZeroException {
// getting values from temporary registers
BigInteger rs = new BigInteger(TR[RS_FIELD].getHexString(), 16);
BigInteger rt = new BigInteger(TR[RT_FIELD].getHexString(), 16);
// performing operations
BigInteger result[] = null;
try {
result = rs.divideAndRemainder(rt);
} catch (ArithmeticException e) {
if (cpu.isEnableForwarding()) {
cpu.getLO().decrWriteSemaphore();
cpu.getHI().decrWriteSemaphore();
}
throw new DivisionByZeroException();
}
// writing result in temporary registers
String tmp = result[0].toString(2); // quotient
while (tmp.length() < 64) {
tmp = "0" + tmp;
}
TR[LO_REG].setBits(tmp, 0);
tmp = result[1].toString(2); // reminder
while (tmp.length() < 64) {
tmp = "0" + tmp;
}
TR[HI_REG].setBits(tmp, 0);
if (cpu.isEnableForwarding()) {
doWB();
}
}
/**
* @param string0 .equals("135")
* @param string1 .equals("20")
* @param catchCount ==0
*/
public static void test(String string0, String string1, int catchCount) {
try {
new BigInteger("Togliere sta roba");
} catch (NumberFormatException ex) {
catchCount++;
}
try {
new BigInteger((String) null);
} catch (NullPointerException ex) {
catchCount++;
}
Assertions.checkEquals(2, catchCount);
BigInteger bigInteger0 = new BigInteger(string0);
BigInteger bigInteger1 = new BigInteger(string1);
int int0 = bigInteger0.intValue();
int int1 = bigInteger1.intValue();
Assertions.checkEquals(135, int0);
Assertions.checkEquals(20, int1);
BigInteger[] bigIntegerArray0 = bigInteger0.divideAndRemainder(bigInteger1);
BigInteger quotient = bigIntegerArray0[0];
BigInteger remainder = bigIntegerArray0[1];
int quotientInteger = quotient.intValue();
int remainderInteger = remainder.intValue();
Assertions.checkEquals(6, quotientInteger);
Assertions.checkEquals(15, remainderInteger);
BigInteger min = quotient.min(remainder);
Assertions.checkEquals(min.intValue(), quotient.intValue());
}
private void addRemainder(int divisor) {
BigInteger[] newNum = num.divideAndRemainder(BigInteger.valueOf(divisor));
nro.add(Integer.valueOf(newNum[1].intValue()));
num = newNum[0];
}
public String divide(String val1, String val2) {
BigInteger i1 = new BigInteger(val1, 10);
BigInteger i2 = new BigInteger(val2, 10);
return i1.divideAndRemainder(i2)[0].toString(10);
}