Mancala

AtCoder

IDcf17_final_g

Time2000ms

Memory256MB

Difficulty—

Consider the following game: * The game is played using a row of $N$ squares and many stones. * First, $a_i$ stones are put in Square $i\ (1 \leq i \leq N)$. * A player can perform the following operation as many time as desired: "Select an integer $i$ such that Square $i$ contains exactly $i$ stones. Remove all the stones from Square $i$, and add one stone to each of the $i-1$ squares from Square $1$ to Square $i-1$." * The final score of the player is the total number of the stones remaining in the squares. For a sequence $a$ of length $N$, let $f(a)$ be the minimum score that can be obtained when the game is played on $a$. Find the sum of $f(a)$ over all sequences $a$ of length $N$ where each element is between $0$ and $K$ (inclusive). Since it can be extremely large, find the answer modulo $1000000007 (= 10^9+7)$. ## Constraints * $1 \leq N \leq 100$ * $1 \leq K \leq N$ ## Input Input is given from Standard Input in the following format: $N$ $K$ [samples]

Samples

Input #1

2 2

Output #1

10

There are nine sequences of length $2$ where each element is between $0$ and $2$. For each of them, the value of $f(a)$ and how to achieve it is as follows:

*   $f({0,0})$: $0$ (Nothing can be done)
*   $f({0,1})$: $1$ (Nothing can be done)
*   $f({0,2})$: $0$ (Select Square $2$, then Square $1$)
*   $f({1,0})$: $0$ (Select Square $1$)
*   $f({1,1})$: $1$ (Select Square $1$)
*   $f({1,2})$: $0$ (Select Square $1$, Square $2$, then Square $1$)
*   $f({2,0})$: $2$ (Nothing can be done)
*   $f({2,1})$: $3$ (Nothing can be done)
*   $f({2,2})$: $3$ (Select Square $2$)

Input #2

20 17

Output #2

983853488

API Response (JSON)

{
  "problem": {
    "name": "Mancala",
    "description": {
      "content": "Consider the following game: *   The game is played using a row of $N$ squares and many stones. *   First, $a_i$ stones are put in Square $i\\ (1 \\leq i \\leq N)$. *   A player can perform the followin",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "cf17_final_g"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Consider the following game:\n\n*   The game is played using a row of $N$ squares and many stones.\n*   First, $a_i$ stones are put in Square $i\\ (1 \\leq i \\leq N)$.\n*   A player can perform the followin...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments