EXPORT S64 _modPow(S64 value, S64 exponent, S64 modulus)
{
THROWDBG(value < 0, 0xe9170006);
THROWDBG(exponent < 0, 0xe9170006);
THROWDBG(modulus < 0, 0xe9170006);
return (S64)ModPow((U64)value, (U64)exponent, (U64)modulus);
}
//@ Main Function
int main() {
for (int i = 1; i < maxK; i++) invi[i] = ModPow(i, mod - 2);
int _case;
LL n, m, k;
scanf("%d", &_case);
for (int __case = 1; _case; _case--, __case++) {
scanf("%lld%lld%lld", &n, &m, &k);
LL cmk = 1;
for (int i = 1; i <= k; i++)
cmk = cmk * (m - i + 1) % mod * invi[i] % mod;
ck[0] = 1;
for (int i = 1; i <= k; i++)
ck[i] = ck[i - 1] * (k - i + 1) % mod * invi[i] % mod;
LL ans = 0;
for (int i = k, sgn = 1; i >= 1; i--, sgn = -sgn)
ans = (ans + sgn * (i * ModPow(i - 1, n - 1) % mod * ck[i] % mod)) % mod;
ans = (ans + mod) % mod * cmk % mod;
printf("Case #%d: %lld\n", __case, ans);
}
return 0;
}
Shamir::Shares Shamir::split(uint256 secret) const {
Shares shares;
std::vector<CBigNum> coef;
coef.push_back(CBigNum(secret));
for (unsigned char i = 1; i < _quorum; ++i)
coef.push_back(rnd());
for (unsigned char x = 1; x <= _shares; ++x) {
CBigNum accum = coef[0];
for (unsigned char i = 1; i < _quorum; ++i)
accum = (accum + (coef[i] * ModPow(CBigNum(x), i, _order))) % _order;
shares[x] = accum.getuint256();
}
return shares;
}
/* 繰り返し2乗法
* (x ** n) % MODを返す.
* 計算量 log(n) */
Long ModPow(Long x, Long n, Long Mod) {
if (n == 0) return 1;
if (n % 2 == 1) return x * ModPow(x, n - 1, Mod) % Mod;
Long r = ModPow(x, n / 2, Mod);
return r * r % Mod;
}
EXPORT Bool _prime(S64 n)
{
if (n <= 1)
return False;
if ((n & 1) == 0)
return n == 2;
if (n <= 1920000)
{
if (n == 3)
return True;
if (n % 6 != 1 && n % 6 != 5)
return False;
S64 m = n / 6 * 2 + (n % 6 == 1 ? 0 : 1);
size_t size;
const U8* primes_bin = GetPrimesBin(&size);
return (primes_bin[m / 8] & (1 << (m % 8))) != 0;
}
// Miller-Rabin primality test.
U64 enough;
if (n < 2047)
enough = 1;
else if (n < 1373653)
enough = 2;
else if (n < 25326001)
enough = 3;
else if (n < 3215031751)
enough = 4;
else if (n < 2152302898747)
enough = 5;
else if (n < 3474749660383)
enough = 6;
else if (n < 341550071728321)
enough = 7;
else if (n < 3825123056546413051)
enough = 9;
else
{
// n < 2^64 < 318665857834031151167461
enough = 12;
}
{
U64 d = (U64)n - 1;
U64 s = 0;
while ((d & 1) == 0)
{
s++;
d >>= 1;
}
for (U64 i = 0; i < enough; i++)
{
U64 x = ModPow(Primes[i], d, (U64)n);
U64 j;
if (x == 1 || x == (U64)n - 1)
continue;
Bool probablyPrime = False;
for (j = 0; j < s; j++)
{
x = ModPow(x, 2, (U64)n);
if (x == (U64)n - 1)
{
probablyPrime = True;
break;
}
}
if (!probablyPrime)
return False;
}
return True;
}
}