#include <bits/stdc++.h>
#pragma GCC optimize("Ofast")
#pragma GCC optimize("unroll-loops")
using namespace std;
using std::cout;
using std::cin;
using std::endl;
using ll=long long;
using ld=long double;
ll ILL=2167167167167167167;
const int INF=2100000000;
const int mod=998244353;
#define rep(i,a,b) for (ll i=a;i<b;i++)
#define all(p) p.begin(),p.end()
template<class T> using _pq = priority_queue<T, vector<T>, greater<T>>;
template<class T> ll LB(vector<T> &v,T a){return lower_bound(v.begin(),v.end(),a)-v.begin();}
template<class T> ll UB(vector<T> &v,T a){return upper_bound(v.begin(),v.end(),a)-v.begin();}
template<class T> bool chmin(T &a,const T &b){if(a>b){a=b;return 1;}else return 0;}
template<class T> bool chmax(T &a,const T &b){if(a<b){a=b;return 1;}else return 0;}
template<class T> void So(vector<T> &v) {sort(v.begin(),v.end());}
template<class T> void Sore(vector<T> &v) {sort(v.begin(),v.end(),[](T x,T y){return x>y;});}
void yneos(bool a){if(a) cout<<"Yes\n"; else cout<<"No\n";}
template<class T> void vec_out(vector<T> &p){for(int i=0;i<(int)(p.size());i++){if(i) cout<<" ";cout<<p[i];}cout<<"\n";}
template<class T> T vec_min(vector<T> &a){assert(!a.empty());T ans=a[0];for(auto &x:a) chmin(ans,x);return ans;}
template<class T> T vec_max(vector<T> &a){assert(!a.empty());T ans=a[0];for(auto &x:a) chmax(ans,x);return ans;}
template<class T> T vec_sum(vector<T> &a){assert(!a.empty());T ans=a[0]-a[0];for(auto &x:a) ans+=x;return ans;}
int pop_count(long long a){int res=0;while(a){res+=(a&1),a>>=1;}return res;}

ll jyo(ll x,ll y){
	ll res=1;
	while(y){
		res=(res*(1+(x-1)*(y&1)))%mod;
		x=(x*x)%mod;
		y/=2;
	}
	return res;
}



void solve();
// oddloop
int main() {
	ios::sync_with_stdio(false);
	cin.tie(nullptr);
	
	int t=1;
	cin>>t;
	rep(i,0,t) solve();
}

void solve(){
	ll X=(mod-1)/(1<<11);
	ll A,N;
	cin>>A>>N;
	ll ans=0;
	ll Z=1,W=jyo(A,2*X),V=1;
	int m=(N)/X;
	ll b=jyo(W,m),c=1;
	ll d=N-m*X;
	rep(i,0,min(N,X)){
		ll Y=jyo(A,i*i);
		ans+=(Y*(m+(i<d))*(Z==1))%mod;
		Y=(Y*jyo(Z-1,mod-2))%mod;
		Y=(Y*(c+(V-c)*(i<d)-1))%mod;
		ans+=Y;
		c=(c*b)%mod;
		Z=(Z*W)%mod;
		V=(c*Z)%mod;
	}
	cout<<(ans%mod+mod)%mod<<"\n";
	//cout<<(7*17*(1<<23))<<endl;
}