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.

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.

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.

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.

见题面 Input 部分

见题面 Output 部分