#include<vector>
#define cir(i,a,b) for(int i=a;i<b;++i)
using std::vector;
using ulint=unsigned long long;
static constexpr auto MOD=998244353;
static constexpr auto mx=100000007;
vector<unsigned> q(mx);
constexpr auto Inv(ulint x){
    auto res=1ull;auto b=MOD-2;
    while(b){
        if(b&1) (res*=x)%=MOD;
		(x*=x)%=MOD;b>>=1;
	}
	return res;
}
void init(int p){
	q[0]=1;
	cir(i,1,mx) q[i]=(1ull*q[i-1]*i)%MOD;
	auto iv=Inv(q[mx-1]);
	for(auto i=mx-1;i;--i){
	    q[i]=(iv*q[i-1])%MOD;
		iv=(1ull*iv*i)%MOD;
	}
}
int inv(int x){return q[x];}