Replace Digits

AtCoder

IDarc191_a

Time2000ms

Memory256MB

Difficulty—

You are given a string $S$ of length $N$ and a string $T$ of length $M$, both consisting of digits from `1` to `9`. You will perform the following operation for $k=1,2,\ldots,M$ in order: * Choose an integer $i$ such that $1 \le i \le N$. Then, replace the $i$\-th character of $S$ with the $k$\-th character of $T$. Find the maximum possible value of the resulting string $S$ interpreted as an integer after performing the $M$ operations. ## Constraints * $1 \le N,M \le 10^6$ * $N$ and $M$ are integers. * $S$ is a string of length $N$ consisting of digits from `1` through `9`. * $T$ is a string of length $M$ consisting of digits from `1` through `9`. ## Input The input is given from Standard Input in the following format: $N$ $M$ $S$ $T$ [samples]

Samples

Input #1

3 3
191
325

Output #1

593

The following sequence of operations is optimal:

*   For $k=1$: Choose $i=3$. Then, $S =$ `193`.
*   For $k=2$: Choose $i=1$. Then, $S =$ `293`.
*   For $k=3$: Choose $i=1$. Then, $S =$ `593`.

In this case, the value of $S$ interpreted as an integer is $593$, which is the maximum.

Input #2

3 9
191
998244353

Output #2

Input #3

11 13
31415926535
2718281828459

Output #3

98888976555

API Response (JSON)

{
  "problem": {
    "name": "Replace Digits",
    "description": {
      "content": "You are given a string $S$ of length $N$ and a string $T$ of length $M$, both consisting of digits from `1` to `9`. You will perform the following operation for $k=1,2,\\ldots,M$ in order: *   Choose ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc191_a"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given a string $S$ of length $N$ and a string $T$ of length $M$, both consisting of digits from `1` to `9`.\nYou will perform the following operation for $k=1,2,\\ldots,M$ in order:\n\n*   Choose ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments