[SNCPC2019] Digit Mode

Luogu

IDLGP9640

Time3000ms

Memory256MB

DifficultyP5

2019O2优化数位 DP陕西省赛/邀请赛

Let $m(x)$ be the $\textit{mode}$ of the digits in decimal representation of positive integer $x$. The mode is the largest value that occurs most frequently in the sequence. For example, $m(15532)=5$, $m(25252)=2$, $m(103000)=0$, $m(364364)=6$, $m(114514)=1$, $m(889464)=8$. Given a positive integer $n$, DreamGrid would like to know the value of $(\sum\limits_{x=1}^{n} m(x)) \bmod (10^9+7)$. ## Input There are multiple test cases. The first line of the input contains an integer $T$, indicating the number of test cases. For each test case: The first line contains a positive integer $n$ ($1 \le n < 10^{50}$) without leading zeros. It's guaranteed that the sum of $|n|$ of all test cases will not exceed $50$, where $|n|$ indicates the number of digits of $n$ in decimal representation. ## Output For each test case output one line containing one integer, indicating the value of $(\sum\limits_{x=1}^{n} m(x)) \bmod (10^9+7)$. [samples]

Samples

Input #1

Output #1

API Response (JSON)

{
  "problem": {
    "name": "[SNCPC2019] Digit Mode",
    "description": {
      "content": "Let $m(x)$ be the $\\textit{mode}$ of the digits in decimal representation of positive integer $x$. The mode is the largest value that occurs most frequently in the sequence. For example, $m(15532)=5$,",
      "description_type": "Markdown"
    },
    "platform": "Luogu",
    "limit": {
      "time_limit": 3000,
      "memory_limit": 262144
    },
    "difficulty": {
      "LuoguStyle": "P5"
    },
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "LGP9640"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Let $m(x)$ be the $\\textit{mode}$ of the digits in decimal representation of positive integer $x$. The mode is the largest value that occurs most frequently in the sequence. For example, $m(15532)=5$,...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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