Swap 0^X and 1^Y

AtCoder

IDarc194_e

Time2000ms

Memory256MB

Difficulty—

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: $N$ $X$ $Y$ $S$ $T$ [samples]

Samples

Input #1

9 2 1
000111001
011000011

Output #1

Yes

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`.

Input #2

1 1 1
0
1

Output #2

No

It is impossible to make $S$ identical to $T$. Thus, print `No`.

API Response (JSON)

{
  "problem": {
    "name": "Swap 0^X and 1^Y",
    "description": {
      "content": "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",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc194_e"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "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...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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