#pragma GCC optimize("Ofast") #pragma GCC target("avx2") char*mmap(); #define rd_skip() while(*rp++>=48) #define rd(v) int v=0;{int _c;while(_c=*rp++-48,_c>=0)v=v*10+_c;} char wbuf[1<<25]; #define WTHI(v) {long _z=v,_n=0,_d=0;while(++_n,_d=_d<<8|0x30|_z%10,_z/=10);*(long*)wp=_d;wp+=_n;} #define WTLO(v) {long _z=v,_n=8,_d=0;while(_d=_d<<8|0x30|_z%10,_z/=10,--_n);*(long*)wp=_d;wp+=8;} #define wt(v) if(v>=100000000){WTHI(v/100000000);WTLO(v);}else{WTHI(v);} #define MD 1000000007 #define M 400001 int fac[M],ifac[M]; int inverse(int a){ int b=MD; int u=1; int v=0; int s,t; while(b){ t=a/b; s=b; b=a-t*b; a=s; s=v; v=u-t*v; u=s; } if(u<0){ u+=MD; } return u; } void mkfac(){ fac[0]=1; for(int i=1;i