Knot Puzzle

AtCoder

IDagc002_c

Time2000ms

Memory256MB

Difficulty—

We have $N$ pieces of ropes, numbered $1$ through $N$. The length of piece $i$ is $a_i$. At first, for each $i (1≤i≤N-1)$, piece $i$ and piece $i+1$ are tied at the ends, forming one long rope with $N-1$ knots. Snuke will try to untie all of the knots by performing the following operation repeatedly: * Choose a (connected) rope with a total length of at least $L$, then untie one of its knots. Is it possible to untie all of the $N-1$ knots by properly applying this operation? If the answer is positive, find one possible order to untie the knots. ## Constraints * $2≤N≤10^5$ * $1≤L≤10^9$ * $1≤a_i≤10^9$ * All input values are integers. ## Input The input is given from Standard Input in the following format: $N$ $L$ $a_1$ $a_2$ $...$ $a_n$ [samples]

Samples

Input #1

3 50
30 20 10

Output #1

Possible
2
1

If the knot $1$ is untied first, the knot $2$ will become impossible to untie.

Input #2

2 21
10 10

Output #2

Impossible

Input #3

5 50
10 20 30 40 50

Output #3

Possible
1
2
3
4

Another example of a possible solution is $3$, $4$, $1$, $2$.

API Response (JSON)

{
  "problem": {
    "name": "Knot Puzzle",
    "description": {
      "content": "We have $N$ pieces of ropes, numbered $1$ through $N$. The length of piece $i$ is $a_i$. At first, for each $i (1≤i≤N-1)$, piece $i$ and piece $i+1$ are tied at the ends, forming one long rope with $N",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "agc002_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "We have $N$ pieces of ropes, numbered $1$ through $N$. The length of piece $i$ is $a_i$.\nAt first, for each $i (1≤i≤N-1)$, piece $i$ and piece $i+1$ are tied at the ends, forming one long rope with $N...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments