--lucas theorem of number theory

Online proof a lot, although not read ....

The main solution to the case of large combined number of modulus

Baidu Star 2016 1003

First push the formula, then Lucas.

P Very Large case 1e9+7

1#include <iostream>2#include <string>3#include <algorithm>4#include <cstdlib>5#include <cstdio>6#include <Set>7#include <map>8#include <vector>9#include <cstring>Ten#include <stack> One#include <cmath> A#include <queue> - #defineCLC (A, B) memset (A,b,sizeof (a)) -#include <bits/stdc++.h> the Const intMAXN =20005; - Const intinf=0x3f3f3f3f; - Const DoublePi=acos (-1); -typedefLong LongLL; + using namespacestd; - ConstLL MOD = 1e9+7; +  A ll Exp_mod (ll A, ll B, ll P) at { -LL res =1; -      while(b! =0) -     { -         if(b&1) Res = (res * a)%p; -A = (a*a)%p; inb >>=1; -     } to     returnRes; + } -  the ll Comb (ll A, ll B, ll P) * { $     if(A < b)return 0;Panax Notoginseng     if(A = = b)return 1; -     if(b > A) b = A-b; the  +LL ans =1, CA =1, CB =1; A      for(LL i =0; I < b; ++i) the     { +CA = (CA * (a-i))%p; -CB = (CB * (b-i))%p; $     } $Ans = (ca*exp_mod (CB, P-2, p))%p; -     returnans; - } the  -LL Lucas (intNintMintp)Wuyi { theLL ans =1; -  Wu      while(n&&m&&ans) -     { AboutAns = (Ans*comb (n%p, m%p, p))%p; $N/=p; -M/=p; -     } -     returnans; A } +  the intMain () - { $     intN, M; the LL p; the      while(~SCANF ("%d%d", &n, &m)) the     { thep=MOD; -printf"%i64d\n", Lucas (n+m-4, M-2, p)); in     } the     return 0; the}

p at about 100000

HDU 3037

1#include <iostream>2#include <string>3#include <algorithm>4#include <cstdlib>5#include <cstdio>6#include <Set>7#include <map>8#include <vector>9#include <cstring>Ten#include <stack> One#include <cmath> A#include <queue> - #defineCLC (A, B) memset (A,b,sizeof (a)) -#include <bits/stdc++.h> the Const intMAXN =20005; - Const intinf=0x3f3f3f3f; - Const DoublePi=acos (-1); -typedefLong LongLL; + using namespacestd; - //const LL MOD = 1e9+7; +  A ll Powmod (ll a,ll b,ll MOD) { atLL ret=1; -      while(b) { -         if(b&1) ret= (ret*a)%MOD; -A= (a*a)%MOD; -b>>=1; -     } in     returnret; - } toLL fac[100005]; + ll Get_fact (ll p) { -fac[0]=1; the      for(intI=1; i<=p;i++) *Fac[i]= (fac[i-1]*i)%p; $ }Panax Notoginseng ll Lucas (ll n,ll m,ll p) { -LL ret=1; the      while(n&&m) { +LL a=n%p,b=m%p; A         if(A&LT;B)return 0; theRet= (Ret*fac[a]*powmod (fac[b]*fac[a-b]%p,p-2, p))%p; +N/=p; -M/=p; $     } $     returnret; - } - intMain () { the     intT; -scanf"%d",&t);Wuyi      while(t--){ the LL n,m,p; -scanf"%i64d%i64d%i64d",&n,&m,&p); Wu get_fact (p); -printf"%i64d\n", Lucas (n+m,m,p)); About     } $     return 0; -}

--lucas theorem of number theory