Guess the Sum

AtCoder

IDabc355_e

Time2000ms

Memory256MB

Difficulty—

This is an **interactive problem** (where your program interacts with the judge via input and output). You are given a positive integer $N$ and integers $L$ and $R$ such that $0 \leq L \leq R < 2^N$. The judge has a hidden sequence $A = (A_0, A_1, \dots, A_{2^N-1})$ consisting of integers between $0$ and $99$, inclusive. Your goal is to find the remainder when $A_L + A_{L+1} + \dots + A_R$ is divided by $100$. However, you cannot directly know the values of the elements in the sequence $A$. Instead, you can ask the judge the following question: * Choose non-negative integers $i$ and $j$ such that $2^i(j+1) \leq 2^N$. Let $l = 2^i j$ and $r = 2^i (j+1) - 1$. Ask for the remainder when $A_l + A_{l+1} + \dots + A_r$ is divided by $100$. Let $m$ be the minimum number of questions required to determine the remainder when $A_L + A_{L+1} + \dots + A_R$ is divided by $100$ for any sequence $A$. You need to find this remainder within $m$ questions. ## Constraints * $1 \leq N \leq 18$ * $0 \leq L \leq R \leq 2^N - 1$ * All input values are integers. ## Input And Output This is an interactive problem (where your program interacts with the judge via input and output). First, read the integers $N$, $L$, and $R$ from Standard Input: $N$ $L$ $R$ Then, repeat asking questions until you can determine the remainder when $A_L + A_{L+1} + \dots + A_R$ is divided by $100$. Each question should be printed in the following format: $?$ $i$ $j$ Here, $i$ and $j$ must satisfy the following constraints: * $i$ and $j$ are non-negative integers. * $2^i(j+1) \leq 2^N$ The response to the question will be given in the following format from Standard Input: $T$ Here, $T$ is the answer to the question, which is the remainder when $A_l + A_{l+1} + \dots + A_r$ is divided by $100$, where $l = 2^i j$ and $r = 2^i (j+1) - 1$. If $i$ and $j$ do not satisfy the constraints, or if the number of questions exceeds $m$, then $T$ will be `-1`. If the judge returns `-1`, your program is already considered incorrect. In this case, terminate the program immediately. Once you have determined the remainder when $A_L + A_{L+1} + \dots + A_R$ is divided by $100$, print the remainder $S$ in the following format and terminate the program immediately: $!$ $S$ [samples] ## Notes * **At the end of each output, print a newline and flush Standard Output. Otherwise, the verdict may be TLE.** * **If your output is malformed or your program exits prematurely, the verdict will be indeterminate.** * After printing the answer, terminate the program immediately. Otherwise, the verdict will be indeterminate.

API Response (JSON)

{
  "problem": {
    "name": "Guess the Sum",
    "description": {
      "content": "This is an **interactive problem** (where your program interacts with the judge via input and output). You are given a positive integer $N$ and integers $L$ and $R$ such that $0 \\leq L \\leq R < 2^N$. ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc355_e"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "This is an **interactive problem** (where your program interacts with the judge via input and output).\nYou are given a positive integer $N$ and integers $L$ and $R$ such that $0 \\leq L \\leq R < 2^N$. ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments