Ex - Odd Sum

AtCoder

IDabc267_h

Time4000ms

Memory256MB

Difficulty—

You are given a sequence $A=(A_1,A_2,\dots,A_N)$ of length $N$. Find the number, modulo $998244353$, of ways to choose an odd number of elements from $A$ so that the sum of the chosen elements equals $M$. Two choices are said to be different if there exists an integer $i (1 \le i \le N)$ such that one chooses $A_i$ but the other does not. ## Constraints * $1 \le N \le 10^5$ * $1 \le M \le 10^6$ * $1 \le A_i \le 10$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $M$ $A_1$ $A_2$ $\dots$ $A_N$ [samples]

Samples

Input #1

5 6
1 2 3 3 6

Output #1

3

The following $3$ choices satisfy the condition:

*   Choosing $A_1$, $A_2$, and $A_3$.
*   Choosing $A_1$, $A_2$, and $A_4$.
*   Choosing $A_5$.

Choosing $A_3$ and $A_4$ does not satisfy the condition because, although the sum is $6$, the number of chosen elements is not odd.

Input #2

10 23
1 2 3 4 5 6 7 8 9 10

Output #2

API Response (JSON)

{
  "problem": {
    "name": "Ex - Odd Sum",
    "description": {
      "content": "You are given a sequence $A=(A_1,A_2,\\dots,A_N)$ of length $N$. Find the number, modulo $998244353$, of ways to choose an odd number of elements from $A$ so that the sum of the chosen elements equals ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 4000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc267_h"
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  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given a sequence $A=(A_1,A_2,\\dots,A_N)$ of length $N$.\nFind the number, modulo $998244353$, of ways to choose an odd number of elements from $A$ so that the sum of the chosen elements equals ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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