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.