Again ABC String

AtCoder

IDarc147_f

Time2000ms

Memory256MB

Difficulty—

Consider strings of length $N$ consisting of `A`, `B`, and `C`. Among them, find the number of strings that satisfy the following condition, modulo $2$: * Let $S_i$ be the string formed by the first $i$ characters of $S$. Also let $A_i$, $B_i$, and $C_i$ be the numbers of `A`'s, `B`'s, and `C`'s in $S_i$, respectively. For all $i$ such that $1 \le i \le N$, the following holds: * $A_i-B_i \le X$ * $B_i-C_i \le Y$ * $C_i-A_i \le Z$ You have $T$ test cases to solve. ## Constraints * $1 \le T \le 10$ * $1 \le N \le 10^9$ * $0 \le X,Y,Z \le 10^9$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $T$ $\mathrm{case}_1$ $\mathrm{case}_2$ $\vdots$ $\mathrm{case}_T$ Each case is in the following format: $N$ $X$ $Y$ $Z$ [samples]

Samples

Input #1

1
3 2 1 0

Output #1

0

$8$ strings satisfy the condition: `AAB`,`AAC`,`ABA`,`ABC`,`ACA`,`ACB`,`BAA`,`BAC`. Therefore the answer is $0$.

Input #2

10
1 22 9 92
14 7 74 39
23 50 8 6
93 40 9 60
68 8 47 64
11 68 18 24
3 26 54 8
46 17 90 86
86 76 45 55
80 68 79 62

Output #2

API Response (JSON)

{
  "problem": {
    "name": "Again ABC String",
    "description": {
      "content": "Consider strings of length $N$ consisting of `A`, `B`, and `C`. Among them, find the number of strings that satisfy the following condition, modulo $2$: *   Let $S_i$ be the string formed by the firs",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc147_f"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Consider strings of length $N$ consisting of `A`, `B`, and `C`. Among them, find the number of strings that satisfy the following condition, modulo $2$:\n\n*   Let $S_i$ be the string formed by the firs...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments