SS

AtCoder

IDarc077_d

Time2000ms

Memory256MB

Difficulty—

We will call a string that can be obtained by concatenating two equal strings an _even_ string. For example, `xyzxyz` and `aaaaaa` are even, while `ababab` and `xyzxy` are not. For a non-empty string $S$, we will define $f(S)$ as the shortest even string that can be obtained by appending one or more characters to the end of $S$. For example, $f($`abaaba`$)=$`abaababaab`. It can be shown that $f(S)$ is uniquely determined for a non-empty string $S$. You are given an even string $S$ consisting of lowercase English letters. For each letter in the lowercase English alphabet, find the number of its occurrences from the $l$\-th character through the $r$\-th character of $f^{10^{100}} (S)$. Here, $f^{10^{100}} (S)$ is the string $f(f(f( ... f(S) ... )))$ obtained by applying $f$ to $S$ $10^{100}$ times. ## Constraints * $2 \leq |S| \leq 2\times 10^5$ * $1 \leq l \leq r \leq 10^{18}$ * $S$ is an even string consisting of lowercase English letters. * $l$ and $r$ are integers. ## Input Input is given from Standard Input in the following format: $S$ $l$ $r$ [samples]

Samples

Input #1

abaaba
6 10

Output #1

3 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Since $f($`abaaba`$)=$`abaababaab`, the first ten characters in $f^{10^{100}}(S)$ is also `abaababaab`. Thus, the sixth through the tenth characters are `abaab`. In this string, `a` appears three times, `b` appears twice and no other letters appear, and thus the output should be $3$ and $2$ followed by twenty-four $0$s.

Input #2

xx
1 1000000000000000000

Output #2

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1000000000000000000 0 0

Input #3

vgxgpuamkvgxgvgxgpuamkvgxg
1 1000000000000000000

Output #3

87167725689669676 0 0 0 0 0 282080685775825810 0 0 0 87167725689669676 0 87167725689669676 0 0 87167725689669676 0 0 0 0 87167725689669676 141040342887912905 0 141040342887912905 0 0

API Response (JSON)

{
  "problem": {
    "name": "SS",
    "description": {
      "content": "We will call a string that can be obtained by concatenating two equal strings an _even_ string. For example, `xyzxyz` and `aaaaaa` are even, while `ababab` and `xyzxy` are not. For a non-empty string ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc077_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "We will call a string that can be obtained by concatenating two equal strings an _even_ string. For example, `xyzxyz` and `aaaaaa` are even, while `ababab` and `xyzxy` are not.\nFor a non-empty string ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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