Problem:
Score : 100 points

Problem Statement

There are N children, numbered 1, 2, \ldots, N.

They have decided to share K candies among themselves.
Here, for each i (1 \leq i \leq N), Child i must receive between 0 and a_i candies (inclusive).
Also, no candies should be left over.

Find the number of ways for them to share candies, modulo 10^9 + 7.
Here, two ways are said to be different when there exists a child who receives a different number of candies.

Constraints

All values in input are integers.

1 \leq N \leq 100

0 \leq K \leq 10^5

0 \leq a_i \leq K

Input

Input is given from Standard Input in the following format:

N K
a_1 a_2 \ldots a_N

Output

Print the number of ways for the children to share candies, modulo 10^9 + 7.

Sample Input 1

3 4
1 2 3

Sample Output 1

5

There are five ways for the children to share candies, as follows:

(0, 1, 3)

(0, 2, 2)

(1, 0, 3)

(1, 1, 2)

(1, 2, 1)

Here, in each sequence, the i-th element represents the number of candies that Child i receives.

Sample Input 2

1 10
9

Sample Output 2

0

There may be no ways for the children to share candies.

Sample Input 3

2 0
0 0

Sample Output 3

1

There is one way for the children to share candies, as follows:

(0, 0)

Sample Input 4

4 100000
100000 100000 100000 100000

Sample Output 4

665683269

Be sure to print the answer modulo 10^9 + 7.

Solution in C++ (GCC 9.2.1) (judge verdict: Runtime Error)

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

typedef int in;
#define int long long
int MAX=1e9;
int MAXEST=1e18;
int MOD=1e9+7;

int n,k;
int a[105];
int dp[105][10005];

int f(int idx,int rem)
{
    if(idx==n)
    {
        return (rem==0);
    }
    int &ret=dp[idx][rem];
    if(ret!=-1)
        return ret;
    ret=0;
    for(int i=0;i<=a[idx];i++){
        if(rem-i>=0){
            ret+=f(idx+1,rem-i);
            ret%=MOD;
        }
    }
    return ret%MOD;
}

in main()
{
    int tc=1;
//    cin>>tc;
    while(tc--)
    {
        cin>>n>>k;
        for(int i=0;i<n;i++){
            cin>>a[i];
        }
        memset(dp,-1,sizeof dp);
        cout<<f(0,k)%MOD<<endl;
    }
    return 0;
}