Partition

AtCoder

IDarc179_a

Time2000ms

Memory256MB

Difficulty—

You are given integers $N$ and $K$. The **cumulative sums** of an integer sequence $X=(X_1,X_2,\dots ,X_N)$ of length $N$ is defined as a sequence $Y=(Y_0,Y_1,\dots ,Y_N)$ of length $N+1$ as follows: * $Y_0=0$ * $Y_i=\displaystyle\sum_{j=1}^{i}X_j\ (i=1,2,\dots ,N)$ An integer sequence $X=(X_1,X_2,\dots ,X_N)$ of length $N$ is called a **good sequence** if and only if it satisfies the following condition: * Any value in the cumulative sums of $X$ that is less than $K$ appears before any value that is not less than $K$. * Formally, for the cumulative sums $Y$ of $X$, for any pair of integers $(i,j)$ such that $0 \le i,j \le N$, if $(Y_i < K$ and $Y_j \ge K)$, then $i < j$. You are given an integer sequence $A=(A_1,A_2,\dots ,A_N)$ of length $N$. Determine whether the elements of $A$ can be rearranged to a good sequence. If so, print one such rearrangement. ## Constraints * $1 \leq N \leq 2 \times 10^5$ * $-10^9 \leq K \leq 10^9$ * $-10^9 \leq A_i \leq 10^9$ * All input values are integers. ## Input The input is given from Standard Input in the following format: $N$ $K$ $A_1$ $A_2$ $\cdots$ $A_N$ [samples]

Samples

Input #1

4 1
-1 2 -3 4

Output #1

Yes
-3 -1 2 4

If you rearrange $A$ to $(-3,-1,2,4)$, the cumulative sums $Y$ in question will be $(0,-3,-4,-2,2)$. In this $Y$, any value less than $1$ appears before any value not less than $1$.

Input #2

4 -1
1 -2 3 -4

Output #2

No

Input #3

10 1000000000
-1000000000 -1000000000 -1000000000 -1000000000 -1000000000 1000000000 1000000000 1000000000 1000000000 1000000000

Output #3

Yes
-1000000000 -1000000000 -1000000000 -1000000000 -1000000000 1000000000 1000000000 1000000000 1000000000 1000000000

API Response (JSON)

{
  "problem": {
    "name": "Partition",
    "description": {
      "content": "You are given integers $N$ and $K$. The **cumulative sums** of an integer sequence $X=(X_1,X_2,\\dots ,X_N)$ of length $N$ is defined as a sequence $Y=(Y_0,Y_1,\\dots ,Y_N)$ of length $N+1$ as follows: ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc179_a"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given integers $N$ and $K$.\nThe **cumulative sums** of an integer sequence $X=(X_1,X_2,\\dots ,X_N)$ of length $N$ is defined as a sequence $Y=(Y_0,Y_1,\\dots ,Y_N)$ of length $N+1$ as follows:\n...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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