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.

Examples

Input

3 4
1 2 3


Output

5


Input

1 10
9


Output

0


Input

2 0
0 0


Output

1


Input

4 100000
100000 100000 100000 100000


Output

665683269
import java.io.*; 
import java.util.*; 
//import javafx.util.*; 
import java.math.*;
//import java.lang.*;
public class Main 
{ 
    
    // static int n;static ArrayList<Integer> arr[];
    // static int m;
    // static boolean v[];
   // int ans[];
 
    public static void main(String[] args) throws IOException { 
    //    Scanner sc=new Scanner(System.in);
        PrintWriter pw = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
        br = new BufferedReader(new InputStreamReader(System.in));
        int n=nextInt();
        int k=nextInt();
        int m=1000000007;
        int arr[]=new int[n];
        for(int i=0;i<n;i++){
            arr[i]=nextInt();
        }
        int dp[]=new int[k+1];
        dp[0]=1;
        for(int i=0;i<n;i++){
            int add[]=new int[k+1];
            for(int used=k-1;used>=0;used--){
                int l=used+1;
                int r=used+Math.min(k-used,arr[i]);
                add[l]=(add[l]+dp[used])%m;
                if(r<k){
                    add[r+1]=add[r+1]-dp[used];
                    if(add[r+1]<0){
                        add[r+1]+=m;
                    }
                }

            }
            int prefix=0;
            for(int j=0;j<=k;j++){
                prefix=(prefix+add[j])%m;
                dp[j]=(dp[j]+prefix)%m;
            }

        }
        pw.println(dp[k]);
        pw.close();

    }
    public static BufferedReader br;
    public static StringTokenizer st;
    public static String next() {
        while (st == null || !st.hasMoreTokens()) {
       try {
                st = new StringTokenizer(br.readLine());
            } catch (Exception e) {
                throw new RuntimeException(e);
            }
        }
        return st.nextToken();
    }
 
    public static Integer nextInt() {
        return Integer.parseInt(next());
    }
 
    public static Long nextLong() {
        return Long.parseLong(next());
    }
 
    public static Double nextDouble() {
        return Double.parseDouble(next());
    }
    static class Pair{
        String x;int y;int z;
        Pair(String x,int y,int z){
            this.x=x;
            this.y=y;
            this.z=z;
         //   this.z=z;
          //  this.i=i;
        }
    }
    static class sorting implements Comparator<Pair>{
        public int compare(Pair a,Pair b){
            //return (a.y)-(b.y);
            if(a.y==b.y){
                return -1*(a.z-b.z);
            }
            return (a.y-b.y);
        }
    }
    public static int[] na(int n)throws IOException{
        int[] a = new int[n];
        for(int i = 0;i < n;i++)a[i] = nextInt();
        return a;
    }
    static class query implements Comparable<query>{
        int l,r,idx,block;
        static int len;
        query(int l,int r,int i){
            this.l=l;
            this.r=r;
            this.idx=i;
            this.block=l/len;
        }   
        public int compareTo(query a){
            return block==a.block?r-a.r:block-a.block;
        }
    }
    static boolean isPrime(int n) { 
        if (n <= 1) 
            return false; 
        if (n <= 3) 
            return true; 
        if (n % 2 == 0 ||  
            n % 3 == 0) 
            return false; 
      
        for (int i = 5; 
                 i * i <= n; i = i + 6) 
            if (n % i == 0 || 
                n % (i + 2) == 0) 
                return false; 
      
        return true; 
    } 
    static int gcd(int a, int b) { 
      if (b == 0) 
        return a; 
      return gcd(b, a % b);  
    }  
    // static long modInverse(long a, long m) { 
    //     long g = gcd(a, m); 
    //     if (g != 1) 
    //         return -1; 
    //     else{ 
    //         // If a and m are relatively prime, then modulo inverse 
    //         // is a^(m-2) mode m 
    //         return (power(a, m - 2, m)); 
    //     } 
    // } 
      
    // To compute x^y under modulo m 
    static long power(long x, long y, long m){ 
        if (y == 0) 
            return 1;      
        long p = power(x, y / 2, m) % m; 
        p = (p * p) % m; 
      
        if (y % 2 == 0) 
            return p; 
        else
            return (x * p) % m; 
    }
    static long fast_pow(long base,long n,long M){
        if(n==0)
           return 1;
        if(n==1)
        return base;
        long halfn=fast_pow(base,n/2,M);
        if(n%2==0)
            return ( halfn * halfn ) % M;
        else
            return ( ( ( halfn * halfn ) % M ) * base ) % M;
    }
       static long modInverse(long n,int M){
        return fast_pow(n,M-2,M);
    }
    
} 