BigInt calculate_result(const BigInt c1,
const BigInt c2,
const BigInt d1,
const BigInt d2,
const BigInt order)
{
BigInt numerator, denominator, result;
if(d1 == d2) {
printf("Cannot calculate the discrete log\n");
return -1;
}
/* numerator = (c1 - c2) mod order */
numerator = (c1 - c2) % order;
if(numerator < 0) numerator += order;
/* denominator (d2 - d1)^(-1) mod order */
denominator = (d2 - d1) % order;
if(denominator < 0) denominator += order;
denominator = modInverse(denominator, order);
/* result */
result = (numerator * denominator) % order;
return result;
}
int main()
{
fact[0]=1;
for(long long i = 1; i <=1000001; i++ )
fact[i] = (fact[i-1]*i)%mod;
int t,tt=1;
scanf("%d",&t);
while(tt<=t){
long long n,r,mult,inv,rslt;
scanf("%lld %lld",&n,&r);
if(r==0||n==r)
{
printf("Case %d: 1\n",tt++);
continue;
}
mult=(fact[r]*fact[n-r])%mod;
inv = modInverse(mult,mod);
rslt=(fact[n]*inv)%mod;
printf("Case %d: %lld\n",tt++,rslt);
}
return 0;
}
void MainWindow::Inverter()
{
int modmul = modInverse(ui->A->currentText().toInt(), 26);
int modadd = 26 - ((ui->B->currentText().toInt() * modmul) % 26);
ui->A->setCurrentText(QString::number(modmul));
ui->B->setCurrentText(QString::number(modadd));
}
// use lagrange polynomials to find f(0) of the curve, which is the secret number
TINT JoinShares(const TShares& shares) const
{
// make sure there is at elast the minimum number of shares
assert(shares.size() >= size_t(c_sharesNeeded));
// Sigma summation loop
TINT sum = 0;
for (TINT j = 0; j < c_sharesNeeded; ++j)
{
TINT y_j = shares[(size_t)j][1];
TINT numerator = 1;
TINT denominator = 1;
// Pi product loop
for (TINT m = 0; m < c_sharesNeeded; ++m)
{
if (m == j)
continue;
numerator = (numerator * shares[(size_t)m][0]) % c_prime;
denominator = (denominator * (shares[(size_t)m][0] - shares[(size_t)j][0])) % c_prime;
}
sum = (c_prime + sum + y_j * numerator * modInverse(denominator, c_prime)) % c_prime;
}
return sum;
}
int join_shares(int *xy_pairs, int n) {
int secret = 0;
long numerator;
long denominator;
long startposition;
long nextposition;
long value;
int i;
int j;
for (i = 0; i < n; ++i)
{
numerator = 1;
denominator = 1;
for (j = 0; j < n; ++j)
{
if(i != j) {
startposition = xy_pairs[i*2];
nextposition = xy_pairs[j*2];
numerator = (numerator * -nextposition) % prime;
denominator = (denominator * (startposition - nextposition)) % prime;
}
}
value = xy_pairs[i * 2 + 1];
secret = (secret + (value * numerator * modInverse(denominator))) % prime;
}
/* Sometimes we're getting negative numbers, and need to fix that */
secret = (secret + prime) % prime;
return secret;
}
//сложение точки P c собой же
ECPoint ECPoint::Double(ECPoint & pnt)
{
ECPoint *p2 = new ECPoint();
(*p2).a = pnt.a;
(*p2).b = pnt.b;
(*p2).p = pnt.p;
mpz_class dy = 3 * pnt.x * pnt.x + pnt.a;
mpz_class dx = 2 * pnt.y;
if (dx < 0)
dx += pnt.p;
if (dy < 0)
dy += pnt.p;
mpz_class m = (dy * modInverse(dx, pnt.p)) % pnt.p;
(*p2).x = (m * m - pnt.x - pnt.x) % pnt.p;
(*p2).y = (m * (pnt.x - (*p2).x) - pnt.y) % pnt.p;
if ((*p2).x < 0)
(*p2).x += pnt.p;
if ((*p2).y < 0)
(*p2).y += pnt.p;
return (*p2);
}
//сложение двух точек P1 и P2
ECPoint operator+(ECPoint & p1, ECPoint & p2)
{
ECPoint *p3 = new ECPoint();
p3->a = p1.a;
p3->b = p1.b;
p3->p = p1.p;
mpz_class dy = p2.y-p1.y;
mpz_class dx = p2.x-p1.x;
if (dx < 0)
dx = dx + p1.p;
if (dy < 0)
dy = dy + p1.p;
mpz_class alpha = (dy * modInverse(dx,p1.p)) % p1.p;
if (alpha < 0)
alpha = alpha + p1.p;
(*p3).x = (alpha * alpha - p1.x - p2.x) % p1.p;
(*p3).y = (-p1.y + alpha * (p1.x - (*p3).x)) % p1.p;
if ((*p3).x < 0)
(*p3).x += p1.p;
if ((*p3).y < 0)
(*p3).y += p1.p;
return *p3;
}
void add_different()
{
temp=(((y_q-y_p)%p)*modInverse(x_q-x_p,p))%p;
lambda = temp;//modInverse(temp,p);
x_r = (pow(lambda,2)-x_p-y_p);
x_r = x_r%p;
y_r = (lambda*(x_p - x_r)- y_p) % p;
printf("\n\n\tResultant x = %d\n\tResultant Y = %d",x_r,y_r);
}
//precomputes factorial modulo M and inverse Facctorial modulo M
void pre_fact() {
invFact[0] = 1;
fact[0] = 1;
for ( lli i = 1; i <= LIM; i++ ) {
fact[i] = (fact[i-1]*i)%M;
invFact[i] = (invFact[i-1]*modInverse(i,M)) % M;
}
return;
}
int InversiveGenerator::operator() (){
int randomNumber;
if(this->getSeed() == 0){
randomNumber = this->b;
}else{
randomNumber = (a*modInverse(this->getSeed(), this->getMax() )+b) % getMax();
}
randomNumber = this->getMin() + randomNumber % (this->getMax()-this->getMin()+1);
this->setSeed(randomNumber);
return randomNumber;
}
void publickey(int n)
{
xq = xp;
yq = yp;
for(int i = 0; i<n-1; i++)
{
if(xp == xq && yp == yq)
{
temp = (3*pow(xp,2)) + a;
temp = temp%p;
lambda = (temp*modInverse(2*yp,p))%p;
}
else
{
temp = (((yq-yp)%p)*modInverse(xq-xp,p))%p;
lambda = temp;
}
xr = (pow(lambda,2)-xp-xq);
xr = xr%p;
yr = (lambda*(xp-xr)-yp)%p;
if(xr<0)
{
xr=p+xr;
}
if(yr<0)
{
yr=p+yr;
}
xq = xr;
yq = yr;
}
}
int main(void) {
int t,n,i,mi;
fact[0]=1;
scanf("%d",&t);
for(i=1;i<=2*1000000;i++){fact[i]=i*fact[i-1];fact[i]%=MOD;}
while(t--){
scanf("%d",&n);
mi=(int)((fact[n-1]*fact[n-1])%MOD);
mi=modInverse(mi);
ans=(mi*fact[2*n-1]);
if(ans>MOD)ans%=MOD;
printf("%lld\n",ans);
}
return 0;
}
/*
* 解密
*
* @param key 密钥 { a, b }
* @param src 待解密的字符串
* @param dest 经过解密后的字符串
*/
char * decrypt(int* key, char* src, char* dest)
{
char *pSrc = src;
char *pDest = dest;
int arr[2] = { modInverse(key[0], WIDTH), -key[1] };
for (int i = 0; *pSrc; ++i, ++pSrc, ++pDest)
{
if (!isalpha(*pSrc))
continue;
*pDest = unshift(arr, toupper(*pSrc));
}
return dest;
}
//обратное превращение числа из СОК в традиционную десятичную алгебру
//происходит по Китайской теореме об остатках (см. RNS theory, p 216)
mpz_class RNSNumber::getConventionalNumber()
{
mpz_class Mtot;
Mtot = 1;
for(int i = 0; i < this->system.base.size(); ++i)
Mtot *= this->system.base[i];
std::vector<mpz_class> M;
std::vector<mpz_class> Minv;
for(int i = 0; i < this->system.base.size(); ++i)
{
M.push_back(Mtot/this->system.base[i]);
Minv.push_back(modInverse(M[i], this->system.base[i]));
}
mpz_class SUM;
SUM = 0;
for(int i = 0; i < this->system.base.size(); ++i)
{
SUM += this->residues[i] * M[i] * Minv[i];
}
return SUM%Mtot;
}
void add_same()
{
temp = (3*(pow(x_p,2)) + 9);
temp = temp % p;
lambda=( temp *modInverse(2*y_p,p)) %p;
//lambda = modInverse(temp,p);
printf("%d",lambda);
x_r = (pow(lambda,2)-x_p-y_p);
x_r = x_r%p;
while(x_r<=0)
{
x_r=x_r+p;
}
y_r = (lambda*(x_p - x_r)- y_p) % p;
while(y_r<=0)
{
y_r=y_r+p;
}
printf("\n\n\tResultant x = %d\n\tResultant Y = %d",x_r,y_r);
}
int main(int argc, char * * argv)
{
unsigned long p, q;
unsigned long x, n, d, e;
unsigned long i;
FILE *pub = fopen("rsa.pub", "wb");
FILE *pri = fopen("rsa.pri", "wb");
bool found = false;
bool random = true;
bool debug = false;
random = argc > 1 ? false : true;
srand(time(0));
if (random)
{
p = rand() % 16383;
printf("Using p=%lu\n", p);
while (!isprime(p))
{
p++;
}
while (q < p)
{
q = rand() % 16383 + 16380;
}
printf("Using q=%lu\n", q);
while (!isprime(q))
{
q++;
}
}
else
{
printf("P (prime): ");
scanf("%lu", &p);
printf("Q (prime): ");
scanf("%lu", &q);
}
n = p*q;
x = totient(p, q);
srand(time(0));
for (i = rand() % x; i < x && !found; i++)
{
if (isprime(i) && x % i != 0)
{
e = i;
found = true;
}
}
//printf("E (coprime): ");
//scanf("%lu", &e);
d = modInverse(e, x);
printf("Public: n=%lu\te=%lu\n", n, e);
printf("Private: n=%lu\td=%lu\n", n, d);
fwrite(&n, sizeof(unsigned long), 1, pub);
fwrite(&n, sizeof(unsigned long), 1, pri);
fwrite(&e, sizeof(unsigned long), 1, pub);
fwrite(&d, sizeof(unsigned long), 1, pri);
fflush(pub);
fflush(pri);
fclose(pub);
fclose(pri);
if (debug)
{
printf("p=%lu\tq=%lu\tn=%lu\n"
"x=%lu\td=%lu\n\n",
p, q, n, x, d);
}
printf("Testing with value '15'\n");
unsigned long int enc = 0;
enc = encrypt(15, n, e);
printf("Encrypted: %lu\t", enc);
enc = decrypt(enc, n, d);
printf("Decrypted: %lu\n", enc);
return 0;
}
void dhke()
{
printf("\n\n\tENTER THE VALUES OF Xg AND Yg : ");
scanf("%d%d",&x_g,&y_g);
na = rand()%10+2;
nb = rand()%10+2;
//public key of A
x_r = x_g;
y_r = y_g;
for(i=0;i<na-1;i++)
{
if(x_g == x_r && y_g == y_r)
{
temp = (3*(pow(x_g,2)) + 9);
temp = temp % p;
lambda=( temp *modInverse(2*y_g,p)) %p;
}
else
{
temp=(((y_r-y_g)%p)*modInverse(x_r-x_g,p))%p;
lambda = temp;//modInverse(temp,p);
}
x_r = (pow(lambda,2)-x_g-x_r);
x_r = x_r%p;
y_r = (lambda*(x_g - x_r)- y_g) % p;
}
pa_x = x_r;
pa_y = y_r;
//public key of B
x_r = x_g;
y_r = y_g;
for(i=0;i<nb-1;i++)
{
if(x_g == x_r && y_g == y_r)
{
temp = (3*(pow(x_g,2)) + 9);
temp = temp % p;
lambda=( temp *modInverse(2*y_g,p)) %p;
}
else
{
temp=(((y_r-y_g)%p)*modInverse(x_r-x_g,p))%p;
lambda = temp;//modInverse(temp,p);
}
x_r = (pow(lambda,2)-x_g-x_r);
x_r = x_r%p;
y_r = (lambda*(x_g - x_r)- y_g) % p;
}
pb_x = x_r;
pb_y = y_r;
//secret key of A
x_r = pb_x;
y_r = pb_y;
for(i=0;i<na;i++)
{
if(x_g == x_r && y_g == y_r)
{
temp = (3*(pow(x_g,2)) + 9);
temp = temp % p;
lambda=( temp *modInverse(2*y_g,p)) %p;
}
else
{
temp=(((y_r-y_g)%p)*modInverse(x_r-x_g,p))%p;
lambda = temp;//modInverse(temp,p);
}
x_r = (pow(lambda,2)-x_g-x_r);
x_r = x_r%p;
y_r = (lambda*(x_g - x_r)- y_g) % p;
}
ka_x = x_r;
ka_y = y_r;
//secret of b
x_r = pa_x;
y_r = pa_y;
for(i=0;i<nb;i++)
{
if(x_g == x_r && y_g == y_r)
{
temp = (3*(pow(x_g,2)) + 9);
temp = temp % p;
lambda=( temp *modInverse(2*y_g,p)) %p;
}
else
{
temp=(((y_r-y_g)%p)*modInverse(x_r-x_g,p))%p;
lambda = temp;//modInverse(temp,p);
}
x_r = (pow(lambda,2)-x_g-x_r);
x_r = x_r%p;
y_r = (lambda*(x_g - x_r)- y_g) % p;
}
kb_x = x_r;
kb_y = y_r;
if(ka_x == kb_x && ka_y == kb_y)
{
printf("\n\n\tSUCESS EXCHANGE");
}
else
{
printf("\n\n\tWRONG EXCHANGE");
}
}
