#pragma GCC target("avx2")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")

#include<bits/stdc++.h>
#include<atcoder/all>
using namespace std;
using namespace atcoder;

typedef modint998244353 mint;
typedef long long ll;

vector<mint> poly_inv(vector<mint> &a, int M = -314159265){
	if (M == -314159265) M = (int)a.size();
	else if (M <= 0) return {};
	int n = a.size();
	mint r = a[0].pow((ll)(mint::mod())-2);
	int m = 1;
	vector<mint> res = {r};
	while (m < M){
		vector<mint> f = a;
		f.resize(2 * m);
		vector<mint> g = res;
		g.resize(2 * m);
		internal::butterfly(f);
		internal::butterfly(g);
		for (int i=0; i<2*m; i++){
			f[i] = f[i] * g[i];
		}
		internal::butterfly_inv(f);
		for (int i=0; i<m; i++){
			f[i] = f[i + m];
		}
		for (int i=0; i<m; i++){
			f[i + m] = 0;
		}
		internal::butterfly(f);
		for (int i=0; i<2*m; i++){
			f[i] = f[i] * g[i];
		}
		internal::butterfly_inv(f);
		mint iz = mint(2*m).inv();
		iz = -iz * iz;
		for (int i=0; i<m; i++){
			f[i] = f[i] * iz;
		}
		res.insert(res.end(), f.begin(), f.begin()+m);
		m <<= 1;
	}
	res.resize(M);
	return res;
}

int ceil_pow2(int n) {
	int x = 0;
	while ((1U << x) < (unsigned int)(n)) x++;
	return x;
}

vector<mint> multi_eval(vector<mint> x, vector<mint> a){
	int n = x.size();
	int siz = 1 << ceil_pow2(n);
	vector<vector<mint>> g(2*siz, vector<mint>{1});
	for (int i=0; i<n; i++) g[i + siz] = {-x[i], 1};
	for (int i=siz-1; i>0; i--) g[i] = convolution(g[2*i], g[2*i+1]);
	vector<mint> f;
	for (int i=1; i<2*siz; i++){
		if (i==1) f = a;
		else f = g[i>>1];
		int fs = f.size(), gs = g[i].size();
		int m = fs - gs + 1;
		vector<mint> v = {}, w = {};
		if (m > 0){
			vector<mint> ft(m);
			for (int j=0; j<m; j++) ft[j] = f[fs-1-j];
			vector<mint> gt(gs);
			for (int j=0; j<gs; j++) gt[j] = g[i][gs-1-j];
			v = convolution(ft, poly_inv(gt, m));
			v.resize(m);
			reverse(v.begin(), v.end());
			w = convolution(v, g[i]);
		}
		g[i] = f;
		for (int j=0; j<w.size(); j++){
			g[i][j] -= w[j];
		}
		while (g[i].size() > 1 && g[i][g[i].size() - 1] == 0){
			g[i].pop_back();
		}
	}
	vector<mint> ret(n);
	for (int i=0; i<n; i++){
		ret[i] = g[i+siz][0];
	}
	return ret;
}

void solve(){
	const int m = 7500;
	//int ax = 998, n = 998244352;
	int ax, n; cin >> ax >> n;
	
	clock_t start = clock();
	clock_t end = clock();     // 終了時間
	
	mint a = ax;
	int r = n / m;

	//cout << m << " " << r << endl;
	mint var = a * a;

	mint ans = 0;
	mint tmp1 = a.pow((ll)2*(m*r)+1);
	mint tmp2 = a.pow((ll)(m*r)*(m*r));
	for (ll i=m*r; i<n; i++){
		ans += tmp2;
		tmp2 *= tmp1;
		tmp1 *= var;
	}

	if (r >= 1){
		vector<mint> f(r);
		vector<mint> g(m);

		tmp1 = a;
		tmp2 = 1;
		for (int i=0; i<r; i++){
			f[i] = tmp2;
			tmp2 *= tmp1;
			tmp1 *= var;
		}

		tmp1 = a.pow((ll)2*r);
		tmp2 = 1;
		for (int i=0; i<m; i++){
			g[i] = tmp2;
			tmp2 *= tmp1;
		}
		
		
		vector<mint> h = multi_eval(g, f);

		mint vvar = a.pow((ll)r * r * 2);
		tmp1 = a.pow((ll)r * r);
		tmp2 = 1;
		for (int i=0; i<m; i++){
			ans += tmp2 * h[i];
			tmp2 *= tmp1;
			tmp1 *= vvar;
		}
	}

	cout << ans.val() << endl;

	end = clock();     // 終了時間
    //std::cout << "duration = " << (double)(end - start) / CLOCKS_PER_SEC << "sec.\n";
	
}

int main(){
	int t; cin >> t;
	while(t--) solve();
}