Problem Statement

You are given two strings $S$ and $T$, each of length $N$ and consisting of 0 and 1, as well as two positive integers $X$ and $Y$. For $i = 1, 2, \ldots, N$, let $S_i$ denote the $i$-th character of $S$.

Determine whether it is possible to make $S$ identical to $T$ by repeatedly performing Operations A and B below any number of times (possibly zero) in any order:

• (Operation A) Choose an integer $i$ satisfying $1 \leq i \leq N-(X+Y)+1$, $S_{i} = S_{i+1} = \cdots = S_{i+X-1} =$ 0, and $S_{i+X} = S_{i+X+1} = \cdots = S_{i+X+Y-1} =$ 1, then change each of $S_{i}, S_{i+1}, \ldots, S_{i+Y-1}$ to 1 and each of $S_{i+Y}, S_{i+Y+1}, \ldots, S_{i+Y+X-1}$ to 0.
• (Operation B) Choose an integer $i$ satisfying $1 \leq i \leq N-(X+Y)+1$, $S_{i} = S_{i+1} = \cdots = S_{i+Y-1} =$ 1, and $S_{i+Y} = S_{i+Y+1} = \cdots = S_{i+Y+X-1} =$ 0, then change each of $S_{i}, S_{i+1}, \ldots, S_{i+X-1}$ to 0 and each of $S_{i+X}, S_{i+X+1}, \ldots, S_{i+X+Y-1}$ to 1.

Constraints

• $1 \leq N \leq 5 \times 10^5$
• $1 \leq X, Y \leq N$
• $S$ and $T$ are strings of length $N$ consisting of 0 and 1.
• All input values are integers.

Input

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

N X Y
S
T

Output

If it is possible to make $S$ identical to $T$, print Yes; otherwise, print No.