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C - Jumping Takahashi

Score : $300$ points

Problem Statement

Takahashi is standing at the coordinate $0$ on a number line.

He will now perform $N$ jumps. In the $i$-th jump $(1 \leq i \leq N)$, he moves $a_i$ or $b_i$ in the positive direction.

Is it possible for him to be at the coordinate $X$ after $N$ jumps?

Constraints

• $1 \leq N \leq 100$
• $1 \leq a_i \lt b_i \leq 100 \, (1 \leq i \leq N)$
• $1 \leq X \leq 10000$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$ $X$

$a_1$ $b_1$

$\vdots$

$a_N$ $b_N$

Output

If it is possible for Takahashi to be at the coordinate $X$ after $N$ jumps, print Yes; otherwise, print No.

2 10
3 6
4 5

Yes

By moving $b_1 (= 6)$ in the first jump and $a_2 (= 4)$ in the second jump, he can be at the coordinate $X (= 10)$.

2 10
10 100
10 100

No

He can be at the coordinate $X (= 10)$ after the first jump, but not after all jumps.

4 12
1 8
5 7
3 4
2 6

Yes