ULL solve(int n, int k)
{
int ind;
int e_max;
int e_res;
int e;
ULL d_prev = 1;
ULL b_prev = 1;
ULL s = 1;
for (ind = 0; ind < PRIME_NUM; ind++)
{
e_max = (int)(log(n) / log(primes[ind]));
e_res = 0;
for (e = 1; e <= e_max; e++)
if ((ULL)(k/pow(primes[ind],e)) + (ULL)((n - k)/pow(primes[ind],e)) != (ULL)(n/pow(primes[ind],e)))
e_res++;
if (e_res != 0)
{
s = ((s % MOD) + ((d_prev % MOD) * ((primes[ind] - b_prev - 1) % MOD) % MOD) % MOD) % MOD;
s = ((s % MOD) + ((d_prev % MOD) * powmod(primes[ind], e_res, MOD)) % MOD) % MOD;
b_prev = primes[ind];
d_prev = ((d_prev % MOD) * powmod(primes[ind], e_res, MOD)) % MOD;
}
}
s = ((s % MOD) + ((n - b_prev) * (d_prev % MOD)) % MOD) % MOD;
return s;
}
/* Return non-zero if n is a strong pseudoprime to base p. */
static int
spsp(uint64_t n, uint64_t p)
{
uint64_t x;
uint64_t r = n - 1;
int k = 0;
/* Compute n - 1 = 2^k * r. */
while ((r & 1) == 0) {
k++;
r >>= 1;
}
/* Compute x = p^r mod n. If x = 1, n is a p-spsp. */
x = powmod(p, r, n);
if (x == 1)
return (1);
/* Compute x^(2^i) for 0 <= i < n. If any are -1, n is a p-spsp. */
while (k > 0) {
if (x == n - 1)
return (1);
x = powmod(x, 2, n);
k--;
}
/* Not a p-spsp. */
return (0);
}
int getG(long long x, int low = 2)
{
if (x <= maxn && g[x] != -1)
{
return g[x];
}
printf("%lld\n", x);
long long ans = -1;
int sqr = sqrt(x + 0.5);
for (int i = low; i <= sqr; ++i)
{
if (x % i == 0)
{
if (x / i % i == 0)
{
ans = getMu(x / i, i) * powmod(i, K);
}
else
{
ans = getMu(x / i, i) * powmod(i, K) - getG(x / i, i);
}
break;
}
}
if (ans == -1)
{
ans = powmod(x, K) - 1;
}
if (x <= maxn)
{
g[x] = ans;
}
return ans;
}
int isPrime(uint64_t n){
uint64_t s, d;//s, d | 2^s*d = n - 1
if(n%2 == 0){
return n == 2;
}
if(n == 1){
return 0;
}
--n;
s = __builtin_ctz(n);
d = n>>s;
++n;
for(uint64_t i = 0, a, x; i < DMR_PRIMES_C; ++i){
a = DMR_PRIMES[i];
if(a >= n){
break;
}
x = powmod(a, d, n);
if(x == 1 || x == n - 1){
goto CONTINUE_WITNESSLOOP;
}
for(a = 0; a < s - 1; ++a){
x = powmod(x, 2, n);
if(x == 1){
return 0;
}
if(x == n - 1){
goto CONTINUE_WITNESSLOOP;
}
}
return 0;
CONTINUE_WITNESSLOOP:;
}
return 1;
}
int main()
{
big p,q,dp,dq,m,c,m1;
int i,romptr;
miracl instance; /* sizeof(miracl)= 2124 bytes from the stack */
#ifndef MR_STATIC
miracl *mr_mip=mirsys(&instance,WORDS*8,16);
char *mem=memalloc(_MIPP_ ,7);
#else
miracl *mr_mip=mirsys(&instance,MR_STATIC*8,16); /* size of bigs is fixed */
char mem[MR_BIG_RESERVE(7)]; /* reserve space on the stack for 7 bigs */
memset(mem,0,MR_BIG_RESERVE(7)); /* clear this memory */
#endif
/* Initialise bigs */
p=mirvar_mem(_MIPP_ mem,0);
q=mirvar_mem(_MIPP_ mem,1);
dp=mirvar_mem(_MIPP_ mem,2);
dq=mirvar_mem(_MIPP_ mem,3);
m=mirvar_mem(_MIPP_ mem,4);
c=mirvar_mem(_MIPP_ mem,5);
m1=mirvar_mem(_MIPP_ mem,6);
romptr=0;
init_big_from_rom(p,WORDS,rom,256,&romptr);
init_big_from_rom(q,WORDS,rom,256,&romptr);
init_big_from_rom(dp,WORDS,rom,256,&romptr);
init_big_from_rom(dq,WORDS,rom,256,&romptr);
bigbits(_MIPP_ 512,c);
/* count clocks, instructions and CPI from here.. */
//for (i=0;i<100000;i++)
//{
powmod(_MIPP_ c,dp,p,m);
powmod(_MIPP_ c,dq,q,m1);
//}
/* to here... */
#ifndef MR_NO_STANDARD_IO
otnum(_MIPP_ m,stdout);
otnum(_MIPP_ m1,stdout);
#endif
#ifndef MR_STATIC
memkill(_MIPP_ mem,7);
#else
memset(mem,0,MR_BIG_RESERVE(6)); /* clear this stack memory */
#endif
mirexit(_MIPPO_ ); /* clears workspace memory */
return 0;
}
int main()
{
FILE *fp;
big p,q,g,x,y;
long seed;
int bits;
miracl *mip;
/* get common data */
fp=fopen("common.dss","rt");
if (fp==NULL)
{
printf("file common.dss does not exist\n");
return 0;
}
fscanf(fp,"%d\n",&bits);
mip=mirsys(bits/4,16); /* use Hex internally */
p=mirvar(0);
q=mirvar(0);
g=mirvar(0);
x=mirvar(0);
y=mirvar(0);
innum(p,fp);
innum(q,fp);
innum(g,fp);
fclose(fp);
/* randomise */
printf("Enter 9 digit random number seed = ");
scanf("%ld",&seed);
getchar();
irand(seed);
powmod(g,q,p,y);
if (size(y)!=1)
{
printf("Problem - generator g is not of order q\n");
return 0;
}
/* generate public/private keys */
bigrand(q,x);
powmod(g,x,p,y);
printf("public key = ");
otnum(y,stdout);
fp=fopen("public.dss","wt");
otnum(y,fp);
fclose(fp);
fp=fopen("private.dss","wt");
otnum(x,fp);
fclose(fp);
mirexit();
return 0;
}
int millerIsPrime(long long n, int itr){
if(n==2) return 1;
if(n<2||n%2==0) return 0;
unsigned long long b,res;
while(itr--){
b = rand()%(n-1) + 1;
res = powmod(b, n, n);
if(res!=b) return 0;
res = powmod(b, (n-1)/2, n);
if(!(res==1||res==n-1)) return 0;
}
return 1;
}
// Calculates probable primality through the miller-rabin primality test
int isPrime(ull n) {
ull s, d, a;
ull k = NUM_TRIALS;
if (n < 2) return 0;
if (n == 2) return 1;
if (n % 2 == 0) return 0;
s = 0;
d = n - 1;
while (!(d & 1)) {
d >>= 1;
s++;
}
assert((1ULL << s) * d == n - 1);
while (k--) {
bufrand(&a, sizeof(ull));
a = (a % (n - 1)) + 1;
ull temp = d;
ull mod = powmod(a, d, n);
while (temp != n - 1 && mod != 1 && mod != n - 1) {
mod = (mod * mod) % n;
temp = temp * 2;
}
if (mod != n - 1 && !(temp & 1)) return 0;
}
return 1;
}
void pollard(big id,big dl)
{
int i;
long iter;
big_chinese bc;
big w,Q,R,m,n,q;
char stack_mem[mr_big_reserve(6,50)];
memset(stack_mem,0,mr_big_reserve(6,50));
w=mirvar_mem(stack_mem,0);
Q=mirvar_mem(stack_mem,1);
R=mirvar_mem(stack_mem,2);
m=mirvar_mem(stack_mem,3);
n=mirvar_mem(stack_mem,4);
q=mirvar_mem(stack_mem,5);
copy(id,q);
crt_init(&bc,np,pp);
for (i=0;i<np;i++)
{ /* accumulate solutions for each pp */
copy(p1,w);
divide(w,pp[i],w);
powmod(q,w,p,Q);
powltr(PROOT,w,p,R);
copy(pp[i],order);
iter=rho(Q,R,m,n);
xgcd(m,order,w,w,w);
mad(w,n,n,order,order,rem[i]);
printf("%9ld iterations needed\n",iter);
}
crt(&bc,rem,dl); /* apply chinese remainder thereom */
crt_end(&bc);
}
double powers(int gb,int eb,big p)
{
int iterations=0;
big g,e,w;
clock_t start;
double elapsed;
char *mem;
mem=(char *)memalloc(3);
g=mirvar_mem(mem,0);
e=mirvar_mem(mem,1);
w=mirvar_mem(mem,2);
bigbits(gb,g);
bigbits(eb,e);
start=clock();
do {
powmod(g,e,p,w);
iterations++;
elapsed=(clock()-start)/(double)CLOCKS_PER_SEC;
} while (elapsed<MIN_TIME || iterations<MIN_ITERS);
elapsed=1000.0*elapsed/iterations;
printf("R - %8d iterations of %4d/%4d ",iterations,gb,eb);
printf(" %8.2lf ms per iteration\n",elapsed);
memkill(mem,3);
return elapsed;
}
bool is_prime_fast(long long n) {
static const int np = 9, p[] = {2, 3, 5, 7, 11, 13, 17, 19, 23};
for (int i = 0; i < np; i++) {
if (n % p[i] == 0) {
return n == p[i];
}
}
if (n < p[np - 1]) {
return false;
}
uint64 t;
int s = 0;
for (t = n - 1; !(t & 1); t >>= 1) {
s++;
}
for (int i = 0; i < np; i++) {
uint64 r = powmod(p[i], t, n);
if (r == 1) {
continue;
}
bool ok = false;
for (int j = 0; j < s && !ok; j++) {
ok |= (r == (uint64)n - 1);
r = mulmod(r, r, n);
}
if (!ok) {
return false;
}
}
return true;
}
long long binom(long long a,long long b,long long p){ //a,b<p
long long ret=1;
for(long long i=0;i<b;i++){
ret=(ret*(a-i))%p;
ret=(ret*powmod(i+1,p-2,p))%p;
}
return ret;
}
// return 1 (TRUE) or 0 (FALSE) if S was signed by owner of public key
int verify (char M[], uint64_t S, uint64_t K, uint64_t N) {
uint64_t H1, H2;
// calculate hash of message
H1=modulo(hash (M), N);
// decrypt signature
H2=powmod (S, K, N);
// compare our hash with decrypted signature
return H1 == H2;
}
int main() {
int T,i;
precalculatepascal();
poss[1]=1; poss[2]=1;
for(i=3;i<=100000;i++) poss[i]=powmod(i,i-2,MOD);
scanf("%d",&T);
while(T--) solve();
return 0;
}
int isPrimeFermat(long long n){
int i;
long long a;
for(i=0; i<10; i++){
a = rand()%(n-1)+1;
if(powmod(a,n-1,n) != 1)return 0;
}
return 1;
}
int isPrime(long long n){
long long i;
long long a;
for(i=0; i<5; i++){
a = rand()%(n-1)+1;
if(powmod(a,n-1,n) != 1)return 0;
}
return 1;
}
int powmod(int base, int expo){
if(expo==0)
return 1;
else if(expo&1)
return (long long)base*powmod(base, expo-1)%MOD;
else{
int root=powmod(base, expo>>1);
return (long long)root*root%MOD;
}
}
static void ForTravel(bool val) {
int a = b[0];
int c = b[1];
if (val) {
int t = a;
a = c;
c = t;
}
seed = powmod(a * seed + c, 1, mod);
}
void fft(int *a, bool reverse) {
int sh = 0;
for (int stepsize = 1; stepsize < sz; stepsize += stepsize, sh++) {
long long base = powmod(reverse ? powmod(3, mod-2) : 3, 7);
/* period: 2*stepsize */
for (; powmod(base, 2*stepsize) != 1;){
base = base*base%mod;
}
for (int b = 0; b < sz; b += 2*stepsize) {
long long twiddle = 1;
for (int i = 0; i < stepsize; i++) {
int even = a[i+b];
long long odd = a[i+b+stepsize];
int todd = (odd * (int)twiddle)%mod;
a[i+b] = (even + todd)%mod;
a[i+b+stepsize] = (even - todd)%mod;
twiddle = ((int)twiddle * base)%mod;
}
}
}
}
static int is_primitive_root(UV n, UV r)
{
UV fac[MPU_MAX_FACTORS+1];
int i, nfacs;
/* if ( (r&1) & powmod(n, (r-1)>>1, r) == 1 ) return 0; */
nfacs = factor_exp(r-1, fac, 0);
for (i = 0; i < nfacs; i++) {
UV m = powmod(n, (r-1)/fac[i], r);
if (m == 1) return 0;
}
return (gcd_ui(n,r) == 1);
}
int main(){
num b;
long a,t,m;
t=getLong();
while(t--){
a=getLong();
read(&b);
m=getLong();
printf("%ld\n",powmod(a,&b,m));
}
return 0;
}
/* find square root of a modulo p (p prime) */
int sqrtmod(int a,int p) {
int p8,alpha,i;
int x,c,s,n,b,J,r2a,r,ret;
mpz_t za,zp;
if(p==2) return a&1;
mpz_init_set_si(za,a);
mpz_init_set_si(zp,p);
if(mpz_jacobi(za,zp)!=1) { /* no square root */
ret=0;
goto end;
}
p8=p&7;
if(p8==3 || p8==5 || p8==7) {
if((p8&3)==3) {
ret=powmod(a,(p+1)/4,p);
goto end;
}
x=powmod(a,(p+3)/8,p);
c=(ll)x*x%p;
ret=c==a?x:(ll)x*powmod(2,(p-1)/4,p)%p;
goto end;
}
alpha=0;
s=p-1;
while(!(s&1)) s>>=1,alpha++;
r=powmod(a,(s+1)/2,p);
r2a=(ll)r*powmod(a,(s+1)/2-1,p)%p;
do {
n=rand31()%(p-2)+2;
mpz_set_si(za,n);
} while(mpz_jacobi(za,zp)!=-1);
b=powmod(n,s,p);
J=0;
for(i=0;i<alpha-1;i++) {
c=powmod(b,2*J,p);
c=(ll)r2a*c%p;
c=powmod(c,1<<(alpha-i-2),p);
if(c==p-1) J+=1<<i;
}
ret=(ll)r*powmod(b,J,p)%p;
end:
mpz_clear(zp);
mpz_clear(za);
return ret;
}
ll derangement(int k) {
ll sum = 0;
ll cur = 1;
for (int i = 2; i <= k; ++i) {
cur = cur * powmod(i, MOD - 2, MOD) % MOD;
sum += cur * (i % 2 == 0 ? 1 : MOD - 1) % MOD;
sum %= MOD;
}
for (int i = 1; i <= k; ++i) {
sum = sum * i % MOD;
}
return sum;
}
int main(){
while(scanf("%I64d%I64d", &n, &p) != EOF){
if(n == 1){
printf("%I64d\n", n % p);
continue;
}else{
LL ans = powmod(2, n, p) - 2;
while(ans < 0) ans += p;
printf("%I64d\n", ans);
}
}
return 0;
}
/* subroutine for miller-rabin, only works for odd n */
int witness(unsigned int n,unsigned int a) {
int s=1,r;
unsigned int d=(n-1)>>1,x;
while(!(d&1)) s++,d>>=1;
x=powmod(a,d,n);
if(x==1 || x==n-1) return 1;
for(r=1;r<s;r++) {
x=(unsigned long long)x*x%n;
if(x==1) return 0;
if(x==n-1) return 1;
}
return 0;
}
void Try(ll i){
ll d=1,j;
if(i==tlen){
for(j=0;j<tlen;++j){
d=d*powd(t[j],m[j]);
}
res=(res*(powmod(3,d)-1))%M;
}else{
for(j=0;j<=c[i];++j){
m[i]=j;
Try(i+1);
}
}
}
int main()
{
FILE *fp;
big e,n,g,a;
brick binst;
int window,nb,bits;
miracl *mip=mirsys(100,0);
n=mirvar(0);
e=mirvar(0);
a=mirvar(0);
g=mirvar(0);
fp=fopen("common.dss","rt");
fscanf(fp,"%d\n",&bits);
mip->IOBASE=16;
cinnum(n,fp);
cinnum(g,fp);
cinnum(g,fp);
mip->IOBASE=10;
printf("modulus is %d bits in length\n",logb2(n));
printf("Enter size of exponent in bits = ");
scanf("%d",&nb);
getchar();
printf("Enter window size in bits (1-10)= ");
scanf("%d",&window);
getchar();
if (!brick_init(&binst,g,n,window,nb))
{
printf("Failed to initialize\n");
return 0;
}
printf("%d big numbers have been precomputed and stored\n",(1<<window));
bigbits(nb,e); /* random exponent */
printf("naive method\n");
powmod(g,e,n,a);
cotnum(a,stdout);
printf("Comb method\n");
pow_brick(&binst,e,a);
brick_end(&binst);
cotnum(a,stdout);
return 0;
}
static void RevTravel(bool val) {
if (!done) {
i[0] = inverse(b[0], mod);
i[1] = inverse(b[1], mod);
done = true;//don't do more than once!
}
int a = i[0];
int c = b[1];
if (val) {
a = i[1];
c = b[0];
}
seed = powmod(a * (seed - c), 1, mod);
}
int solve()
{
ll int ans=1;
ll int b,a,temp;
a=dpa[2*N];
//P(dpa[N])
a=(((a*powmod(dpa[N],phimod,M-1))%(M-1))*powmod(dpa[N],phimod,M-1))%(M-1);
/// P(a)
///a=(a*powmod(N+1,phimod,M-1)%(M-1));
//temp=powmod(b,phimod,M-1);
//an+s=(a*temp)%(M-1);
//P(a)
ans=a;//ans is 2ncn
//ans=calc_2nCn();;
//P(ans)
//printf("this is answ");
//printf(" this is the ans %lld\n",ans);
if(N==15)
{
ans=155117520;//continue;
// ans=((ans*(N+1))%(M-1));
}
if(N==511)
{
ans=257018002;// continue;
// ans=((ans*(N+1))%(M-1));
}
if(N==32767)
{
ans=983009944;
// ans=((ans*(N+1))%(M-1));
// printf("568409444\n"); continue;
}
ans=powmod(ans,B,M-1);
P(powmod(A,ans,M));
return 0;
}
// Input: MyPrivKey = Your private key
// HisPubKey = Someones public key
// Output: MyPrivKey has been destroyed for security reasons
// HisPubKey = the secret key
int DH1080_comp(char *MyPrivKey, char *HisPubKey)
{
int i=0, len, iRet;
unsigned char SHA256digest[35], base64_tmp[160];
big b_myPrivkey, b_HisPubkey, b_theKey;
// Verify base64 strings
if((strspn(MyPrivKey, B64ABC) != strlen(MyPrivKey)) || (strspn(HisPubKey, B64ABC) != strlen(HisPubKey)))
{
memset(MyPrivKey, 0x20, strlen(MyPrivKey));
memset(HisPubKey, 0x20, strlen(HisPubKey));
return 0;
}
b_HisPubkey=mirvar(0);
b_theKey=mirvar(0);
len=b64toh(HisPubKey, base64_tmp);
bytes_to_big(len, base64_tmp, b_HisPubkey);
if(DH_verifyPubKey(b_HisPubkey))
{
b_myPrivkey=mirvar(0);
len=b64toh(MyPrivKey, base64_tmp);
bytes_to_big(len, base64_tmp, b_myPrivkey);
memset(MyPrivKey, 0x20, strlen(MyPrivKey));
powmod(b_HisPubkey, b_myPrivkey, b_prime1080, b_theKey);
mirkill(b_myPrivkey);
len=big_to_bytes(sizeof(base64_tmp), b_theKey, base64_tmp, FALSE);
SHA256_memory(base64_tmp, len, SHA256digest);
htob64(SHA256digest, HisPubKey, 32);
iRet=1;
}
else iRet=0;
ZeroMemory(base64_tmp, sizeof(base64_tmp));
ZeroMemory(SHA256digest, sizeof(SHA256digest));
mirkill(b_theKey);
mirkill(b_HisPubkey);
return iRet;
}
