Lucas定理模板

p为素数，a,b为正整数，并且

a = akp^k+ak-1p^k-1+...+a1p+a0

b = bkp^k+bk-1p^k-1+...+b1p+b0

所有0<=ai,bi<=p-1

C(a,b) = C(ak,bk)*C(ak-1,bk-1)*...*C(a0,b0)%p

fac表示阶乘，inv表示逆元

LL Lucas( LL a , LL b )
{
    LL res = 1;
    while ( a&&b )
    {
        LL aa = a%mod;
        LL bb = b%mod;
        if ( aa<bb ) return 0;
        res = res*fac[aa]%mod*inv[fac[bb]]%mod*inv[fac[aa-bb]]%mod;
        a = a/mod;
        b = b/mod;
    }
    return res;
}