NEQ

AtCoder

IDabc172_e

Time2000ms

Memory256MB

Difficulty—

Count the pairs of length-$N$ sequences consisting of integers between $1$ and $M$ (inclusive), $A_1, A_2, \cdots, A_{N}$ and $B_1, B_2, \cdots, B_{N}$, that satisfy all of the following conditions: * $A_i \neq B_i$, for every $i$ such that $1\leq i\leq N$. * $A_i \neq A_j$ and $B_i \neq B_j$, for every $(i, j)$ such that $1\leq i < j\leq N$. Since the count can be enormous, print it modulo $(10^9+7)$. ## Constraints * $1\leq N \leq M \leq 5\times10^5$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $M$ [samples]

Samples

Input #1

2 2

Output #1

2

$A_1=1,A_2=2,B_1=2,B_2=1$ and $A_1=2,A_2=1,B_1=1,B_2=2$ satisfy the conditions.

Input #2

2 3

Output #2

Input #3

141421 356237

Output #3

881613484

API Response (JSON)

{
  "problem": {
    "name": "NEQ",
    "description": {
      "content": "Count the pairs of length-$N$ sequences consisting of integers between $1$ and $M$ (inclusive), $A_1, A_2, \\cdots, A_{N}$ and $B_1, B_2, \\cdots, B_{N}$, that satisfy all of the following conditions: ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc172_e"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Count the pairs of length-$N$ sequences consisting of integers between $1$ and $M$ (inclusive), $A_1, A_2, \\cdots, A_{N}$ and $B_1, B_2, \\cdots, B_{N}$, that satisfy all of the following conditions:\n\n...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments