Contest Duration: - (local time) (100 minutes) Back to Home
D - Money in Hand /

Time Limit: 3 sec / Memory Limit: 1024 MB

### 制約

• 1\leq N\leq 50
• 1\leq X\leq 10^4
• 1\leq A_i\leq 100
• 1\leq B_i\leq 50
• A_i はすべて異なる。
• 入力はすべて整数

### 入力

N X
A_1 B_1
A_2 B_2
\vdots
A_N B_N


### 入力例 1

2 19
2 3
5 6


### 出力例 1

Yes


### 入力例 2

2 18
2 3
5 6


### 出力例 2

No


### 入力例 3

3 1001
1 1
2 1
100 10


### 出力例 3

Yes


1 枚も使用しない硬貨が存在しても構いません。

Score : 400 points

### Problem Statement

Takahashi has N kinds of coins; specifically, for 1\leq i\leq N, he has B_i coins worth A_i yen (the currency in Japan) each.

Determine if Takahashi can pay exactly X yen (without change) with the coins he currently has.

### Constraints

• 1\leq N\leq 50
• 1\leq X\leq 10^4
• 1\leq A_i\leq 100
• 1\leq B_i\leq 50
• A_i are pairwise distinct.
• All values in the input are integers.

### Input

The input is given from Standard Input in the following format:

N X
A_1 B_1
A_2 B_2
\vdots
A_N B_N


### Output

Print Yes if Takahashi can pay exactly X yen with the coins he currently has; print No otherwise.

### Sample Input 1

2 19
2 3
5 6


### Sample Output 1

Yes


Takahashi has three 2-yen coins and six 5-yen coins. He can use two 2-yen coins and three 5-yen coins to pay exactly 2\times 2+5\times 3=19 yen. Thus, Yes should be printed.

### Sample Input 2

2 18
2 3
5 6


### Sample Output 2

No


There is no combination of the coins that he can use to pay exactly 18 yen. Thus, No should be printed.

### Sample Input 3

3 1001
1 1
2 1
100 10


### Sample Output 3

Yes


He need not use all kinds of coins.