Saving Beans

typedef __int64 LL;
const int M=;
class LUCAS { //lucas Find the combination number C(n,k)%p
LL F[M];
LL inv(LL a,LL mod) {
if(a==) return ;
return inv(mod%a,mod)*(mod-mod/a)%mod;
void init(LL p) {
for(int i=; i<=p; i++) {
LL Lucas(LL n,LL k,LL p) {
LL ans=;
while(n&&k) {
LL a=n%p;
LL b=k%p;
if(a<b) return ;
return ans;
LL solve(LL n,LL k,LL p){
return Lucas(n,k,p);
int main() {
int t,n,m,p;
while(~scanf("%d",&t)) {
while(t--) {
return ;


#define mt(a,b) memset(a,b,sizeof(a))
using namespace std;
typedef __int64 LL;
const int M=;
class LUCASM { // More suitable n,k<=10^9,p<=10^4 The situation of
int flag[M*],prime[],pcnt;
vector<int> rev[M],fac[M];
int quickpow(int a,int b,int c) { // Fast exponentiation (a^b)%c
int ret=%c;
for(; b; a=a*a%c,b>>=) {
if(b&) {
return ret;
void init() {// Just initialize once
for(int i=; i<=; i++) {
if(flag[i]) {
for(int j=; j<pcnt&&prime[j]<=/i; j++) {
if(!(i%prime[j])) break;
for(int i=; i<pcnt; i++) {
int tnum=;
for (int j=; j<prime[i]; j++) {
int now=quickpow(tnum,prime[i]-,prime[i]);
int lucas(int n,int k,int p) {
int ret=;
while (n && k) {
int num1=n%p;
int num2=k%p;
if (num1<num2) return ;
int num=(fac[p][num1]*rev[p][num2])%p;// Calculation c(num1,num2)%p
return ret;
} gx;
int main() {
int n,k,p,cas=;
while(~scanf("%d%d%d",&n,&k,&p)) {
printf("Case #%d: ",cas++);
if(k>n/) k=n-k;
int o=gx.lucas(n+,k,p);
return ;


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