AT_arc194_e [ARC194E] Swap 0^X and 1^Y

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`.

The input is given from Standard Input in the following format: > $ N $ $ X $ $ Y $ $ S $ $ T $

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

### Sample Explanation 1 The following procedure can transform $ S $ into $ T $ : - First, perform Operation A with $ i = 2 $ . Now, $ S = $ `010011001`. - Next, perform Operation B with $ i = 6 $ . Now, $ S = $ `010010011`. - Finally, perform Operation A with $ i = 3 $ . Now, $ S = $ `011000011`. Thus, print `Yes`. ### Sample Explanation 2 It is impossible to make $ S $ identical to $ T $ . Thus, print `No`. ### 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.