Problem Description

The "Hundred Chickens Problem" is a famous mathematical problem from the ancient Chinese text "Zhang Qiujian's Mathematical Manual". The problem states:

"Each rooster costs 5 yuan, each hen costs 3 yuan, and every 3 chicks cost 1 yuan; now with 100 yuan, buying 100 chickens, how many solutions are there?"

Xiao Ming likes this story very much, and he decides to extend this problem and solve it using programming: If each rooster costs \( x \) yuan, each hen costs \( y \) yuan, and every \( z \) chicks cost 1 yuan; now with \( n \) yuan, buying \( m \) chickens, how many solutions are there?

Input Format

The input consists of a single line containing five integers, representing \( x \), \( y \), \( z \), \( n \), and \( m \) as described in the problem. It is guaranteed that \( 1 \le x, y, z \le 10 \) and \( 1 \le n, m \le 1000 \).

Output Format

The output should be a single line containing an integer \( C \), indicating the number of solutions.

Sample Input and Output

Sample Input #1

5 3 3 100 100

Sample Output #1

4

Sample Input #2

1 1 1 100 100

Sample Output #2

5151

Notes

Sample 1 Explanation

This is the "Hundred Chickens Problem" described in the problem. There are 4 solutions:
- 0 roosters, 25 hens, 75 chicks.
- 4 roosters, 18 hens, 78 chicks.
- 8 roosters, 11 hens, 81 chicks.
- 12 roosters, 4 hens, 84 chicks.

见题面 Input 部分

见题面 Output 部分