Linear Equation Of N Variables

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Question Solve Solutions 
1. You are given an array(arr), which represents the coefficients of a linear equation of n variables.
2. You are also given a number, which represents R.H.S of the equation.
   For the equation 3x + 4y + 5z = 15
   Array will be -> [3,4,5] and R.H.S will be -> 15 
3. You have to find the number of non-negative integer solutions of the given equation.

Input Format

A number N arr1 arr2... N numbers A number X

Output Format

Check the sample output and question video.

Constraints

1 <= N <= 10^3
1 <= arr[i] <= 10^3
1 <= X <= 10^4

Example

Input
3
1 2 3
4
Output
4
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