A sly knapsack problem in disguise! Thanks to https://github.com/bhajunsingh/programming-challanges/tree/master/hackerrank/algorithms/the-indian-job
Lesson learnt: The Italian\Indian job is two-way 01 Knapsack. And some complext problem can be converted to a simpler one.

Code is amazingly simple:

#include <cmath>
#include <cstdio>
#include <vector>
#include <iostream>
#include <algorithm>
using namespace std; int knapsack(vector<int> &A, int G)
{
int n = A.size(); vector<int> dp(G + ); for(int i =; i <= n; i ++)
for(int v =G; v >= A[i - ]; v --)
dp[v] = max(dp[v], dp[v- A[i - ]]+ A[i- ]);
return dp[G]; }
int main()
{
int T; cin >> T;
while(T--)
{
// Get input
int N, G;
cin >> N >> G;
vector<int> A(N);
int total = ;
for(int i = ; i < N; i++) {
cin >> A[i];
total += A[i];
} //
if(total > * G)
cout << "NO" << endl;
else
cout << ((total - knapsack(A, G) <= G) ? "YES" : "NO") << endl;
} return ;
}

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