B - Coins

Time Limit: 2 sec / Memory Limit: 256 MB

### 問題文

あなたは、500 円玉を A 枚、100 円玉を B 枚、50 円玉を C 枚持っています。 これらの硬貨の中から何枚かを選び、合計金額をちょうど X 円にする方法は何通りありますか。

### 制約

• 0 \leq A, B, C \leq 50
• A + B + C \geq 1
• 50 \leq X \leq 20,000
• A, B, C は整数である
• X50 の倍数である

### 入力

A
B
C
X


### 入力例 1

2
2
2
100


### 出力例 1

2


• 500 円玉を 0 枚、100 円玉を 1 枚、50 円玉を 0 枚選ぶ。
• 500 円玉を 0 枚、100 円玉を 0 枚、50 円玉を 2 枚選ぶ。

### 入力例 2

5
1
0
150


### 出力例 2

0


### 入力例 3

30
40
50
6000


### 出力例 3

213


Score : 200 points

### Problem Statement

You have A 500-yen coins, B 100-yen coins and C 50-yen coins (yen is the currency of Japan). In how many ways can we select some of these coins so that they are X yen in total?

Coins of the same kind cannot be distinguished. Two ways to select coins are distinguished when, for some kind of coin, the numbers of that coin are different.

### Constraints

• 0 \leq A, B, C \leq 50
• A + B + C \geq 1
• 50 \leq X \leq 20 000
• A, B and C are integers.
• X is a multiple of 50.

### Input

Input is given from Standard Input in the following format:

A
B
C
X


### Output

Print the number of ways to select coins.

### Sample Input 1

2
2
2
100


### Sample Output 1

2


There are two ways to satisfy the condition:

• Select zero 500-yen coins, one 100-yen coin and zero 50-yen coins.
• Select zero 500-yen coins, zero 100-yen coins and two 50-yen coins.

### Sample Input 2

5
1
0
150


### Sample Output 2

0


Note that the total must be exactly X yen.

### Sample Input 3

30
40
50
6000


### Sample Output 3

213