Shuffling

AtCoder

IDarc065_d

Time2000ms

Memory256MB

Difficulty—

There is a string $S$ of length $N$ consisting of characters `0` and `1`. You will perform the following operation for each $i = 1, 2, ..., m$: * Arbitrarily permute the characters within the substring of $S$ starting at the $l_i$\-th character from the left and extending through the $r_i$\-th character. Here, the sequence $l_i$ is non-decreasing. How many values are possible for $S$ after the $M$ operations, modulo $1000000007(= 10^9+7)$? ## Constraints * $2≦N≦3000$ * $1≦M≦3000$ * $S$ consists of characters `0` and `1`. * The length of $S$ equals $N$. * $1≦l_i < r_i≦N$ * $l_i ≦ l_{i+1}$ ## Input The input is given from Standard Input in the following format: $N$ $M$ $S$ $l_1$ $r_1$ : $l_M$ $r_M$ [samples]

Samples

Input #1

Output #1

6

After the first operation, $S$ can be one of the following three: `01001`, `00101` and `00011`.
After the second operation, $S$ can be one of the following six: `01100`, `01010`, `01001`, `00011`, `00101` and `00110`.

Input #2

Output #2

Input #3

11 6
00101000110
2 4
2 3
4 7
5 6
6 10
10 11

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Shuffling",
    "description": {
      "content": "There is a string $S$ of length $N$ consisting of characters `0` and `1`. You will perform the following operation for each $i = 1, 2, ..., m$: *   Arbitrarily permute the characters within the subst",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc065_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There is a string $S$ of length $N$ consisting of characters `0` and `1`. You will perform the following operation for each $i = 1, 2, ..., m$:\n\n*   Arbitrarily permute the characters within the subst...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments