Cubic?

AtCoder

IDabc238_g

Time3000ms

Memory256MB

Difficulty—

Given a sequence $A$ of $N$ numbers, answer the following $Q$ questions. * In the $i$\-th question, you are given integers $L_i$ and $R_i$. Is $A_{L_i} \times A_{L_i+1} \times \dots \times A_{R_i}$ a cubic number? Here, a positive integer $x$ is said to be a cubic number when there is a positive integer $y$ such that $x=y^3$. ## Constraints * All values in input are integers. * $1 \le N,Q \le 2 \times 10^5$ * $1 \le A_i \le 10^6$ * $1 \le L_i \le R_i \le N$ ## Input Input is given from Standard Input in the following format: $N$ $Q$ $A_1$ $A_2$ $\dots$ $A_N$ $L_1$ $R_1$ $L_2$ $R_2$ $\vdots$ $L_Q$ $R_Q$ [samples]

Samples

Input #1

8 5
7 49 30 1 15 8 6 10
1 2
2 3
4 4
5 8
3 8

Output #1

Yes
No
Yes
No
Yes

*   For the first question, $7 \times 49 = 343$ is a cubic number.
*   For the second question, $49 \times 30 = 1470$ is not a cubic number.
*   For the third question, $1$ is a cubic number.
*   For the fourth question, $15 \times 8 \times 6 \times 10 = 7200$ is not a cubic number.
*   For the fifth question, $30 \times 1 \times 15 \times 8 \times 6 \times 10 = 216000$ is a cubic number.

API Response (JSON)

{
  "problem": {
    "name": "Cubic?",
    "description": {
      "content": "Given a sequence $A$ of $N$ numbers, answer the following $Q$ questions. *   In the $i$\\-th question, you are given integers $L_i$ and $R_i$. Is $A_{L_i} \\times A_{L_i+1} \\times \\dots \\times A_{R_i}$",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 3000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc238_g"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Given a sequence $A$ of $N$ numbers, answer the following $Q$ questions.\n\n*   In the $i$\\-th question, you are given integers $L_i$ and $R_i$. Is $A_{L_i} \\times A_{L_i+1} \\times \\dots \\times A_{R_i}$...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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