Toj 4111 combination number modulo violence decomposition

The main idea: the combination of the number of modulo, N and M is not large, p is large and composite.

Idea: Violent decomposition + fast power

Note: Violence is also different, decomposition factorization can use the following work function, written very ingenious, excerpt from the Internet.

1#include <iostream>2#include <cstring>3 using namespacestd;4 5typedefLong Longll;6 Constll mod = 1ll << +;7 Const intN =1000001;8 Const intM =100007;9 BOOLIs_prime[n];Ten intPrime[m]; One intp; A  - void Get() - { thememset (Is_prime,true,sizeof(Is_prime)); -is_prime[0] = is_prime[1] =false; -      for(inti =2; i < N; i++ ) -     { +         if(Is_prime[i]) -         { +             intj = i *i; A             if(J >= N) Break; at              Do -             { -IS_PRIME[J] =false; -J + =i; -} while(J <N); -         } in     } -p =0; to      for(inti =0; i < N; i++ ) +     { -         if(Is_prime[i]) the         { *prime[p++] =i; $         }Panax Notoginseng     } - } the  + ll Pow_mod (ll A, ll N) A { thell ans =1; +A = a%MoD; -      while(n) $     { $         if(N &1 ) -         { -Ans = ans * a%MoD; the         } -n = n >>1;WuyiA = a * a%MoD; the     } -     returnans; Wu } -  About ll Work (ll N, ll Q) $ { -ll ans =0; -      while(n) -     { AAns + = n/Q; +N/=Q; the     } -     returnans; $ } the  the ll C (ll N, ll M) the { thell ans =1; -      for(inti =0; I < P && Prime[i] <= N; i++ ) in     { thell x =Work (n, Prime[i]); thell y = Work (n-m, Prime[i]); Aboutll z =Work (M, Prime[i]); thex = x-(y +z); theAns = ans * pow_mod (Prime[i], x)%MoD; the     } +     returnans; - } the Bayi intMain () the { the     Get(); -     intT; -CIN >>T; the      while(t-- ) the     { the ll N, m; theCIN >> N >>m; -cout << C (n, m) <<Endl; the     } the     return 0; the}

Toj 4111 combination number modulo violence decomposition