//O(1)快速乘
inline LL quick_mul(LL x,LL y,LL MOD){
x=x%MOD,y=y%MOD;
return ((x*y-(LL)(((long double)x*y+0.5)/MOD)*MOD)%MOD+MOD)%MOD;
}
//O(log)快速乘
inline LL quick_mul(LL a,LL n,LL m)
{
LL ans=0;
while(n)
{
if(n&1) ans=(ans+a)%m;
a=(a<<1)%m;
n>>=1;
}
return ans;
}