Problem Statement

You are given non-negative integers $P$ and $B$. Here, $P$ is prime, and $1 \leq B \leq P-1$. For a sequence of non-negative integers $X=(x_1,x_2,\dots,x_n)$, the hash value $\mathrm{hash}(X)$ is defined as follows.

$\displaystyle \mathrm{hash}(X) = \left(\sum_{i=1}^n x_i B^{n-i}\right) \bmod P$

You are given $M$ pairs of integers $(L_1, R_1), (L_2, R_2), \dots, (L_M, R_M)$. Is there a sequence of non-negative integers $A=(A_1, A_2, \dots, A_N)$ of length $N$ that satisfies the condition below?

• For all $i$ $(1 \leq i \leq M)$, the following condition holds:
• Let $s$ be the sequence $(A_{L_i}, A_{L_i + 1}, \dots, A_{R_i})$ obtained by taking the $L_i$-th to the $R_i$-th elements of $A$. Then, $\mathrm{hash}(s) \neq 0$.

Constraints

• $2 \leq P \leq 10^9$
• $P$ is prime.
• $1 \leq B \leq P - 1$
• $1 \leq N \leq 16$
• $1 \leq M \leq \frac{N(N+1)}{2}$
• $1 \leq L_i \leq R_i \leq N$
• $(L_i, R_i) \neq (L_j, R_j)$ if $i \neq j$.
• All input values are integers.

Input

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

P B N M
L_1 R_1
L_2 R_2
\vdots
L_M R_M

Output

If there is a sequence that satisfies the condition in the problem statement, print Yes; otherwise, print No.