#pragma GCC optimize (2)
#include<cstdio>
#include<iostream>
#include<algorithm>
#include<cstring>
#include<cmath>
#include<vector>
#define N 600003
#define ll long long
#define reg register
#define p 998244353
#define pi 3.141592653589793
using namespace std;

inline void read(int &x){
    x = 0;
    char c = getchar();
    while(c<'0'||c>'9') c = getchar();
    while(c>='0'&&c<='9'){
        x = (x<<3)+(x<<1)+(c^48);
        c = getchar();
    }
}

struct coef{
    int v,t;
    inline coef(int _v=0,int _t=0):v(_v),t(_t){}
    inline bool operator < (const coef& rhs) const{
        return t < rhs.t;
    }
};

inline int omega(int x){
    return (3*x*x-x)>>1;
}

int T,n,m,t,tmp,len,sum,ans;
int f[N],g[N],a[N];
coef h[N],_h[N];
ll sup;

int main(){
    scanf("%d",&T);
    m = 300000;
    for(int i=1;omega(i)<=m;i++){
        g[t++] = omega(i);
        g[t++] = omega(-i);
    }
    f[0] = 1;
    for(int i=1;i<=m;i++){
        for(int j=0;j<t&&g[j]<=i;j++)
            f[i] = (f[i]+(ll)(((j>>1)&1)?-1:1)*f[i-g[j]])%p;
    }
    while(T--){
        scanf("%d%d",&n,&m);
        sup = (ll)m*(m+1)>>1;
        t = 0;
        for(int i=1;i<=n;++i){
            scanf("%d",&a[i]);
            t += a[i];
        }
        if(sup-t<m){
            puts("0");
            continue;
        }
        h[0] = coef(1,0);
        h[1] = coef(-1,a[1]);
        len = 1;
        for(int i=2;i<=n;++i){
            tmp = len;
            for(int j=0;j<=tmp;++j){
                if(h[j].t+a[i]>m) break;
                h[++len] = coef(-h[j].v,h[j].t+a[i]);
            }
            sort(h,h+len+1);
            tmp = 0;
            for(int j=0,k=0;;j=k){
                sum = 0;
                while(h[j].t==h[k].t){
                    sum = (sum+h[k].v)%p;
                    ++k;
                }
                _h[tmp++] = coef(sum,h[j].t);
                if(k>len) break;
            }
            len = tmp-1;
            for(int j=0;j<=len;++j) h[j] = _h[j];
        }
        ans = 0;
        for(int i=0;i<=len&&h[i].t<=m;++i)
            ans = (ans+(ll)h[i].v*f[m-h[i].t])%p;
        printf("%d\n",(ans+p)%p);
    }
    return 0;
}