Ex - Popcount Sum

AtCoder

IDabc283_h

Time4000ms

Memory256MB

Difficulty—

Find the sum of popcounts of all integers between $1$ and $N$, inclusive, such that the remainder when divided by $M$ equals $R$. Here, the popcount of a positive integer $X$ is the number of $1$s in the binary notation of $X$, that is, the number of non-negative integers $k$ such that the $2^k$s place is $1$. For each input, process $T$ test cases. ## Constraints * $1 \leq T \leq 10^5$ * $1 \leq M \leq N \leq 10^9$ * $0 \leq R < M$ * All values in the input are integers. ## Input The input is given from Standard Input in the following format. The first line is as follows: $T$ $T$ test cases follow. Each of them is given in the following format: $N$ $M$ $R$ [samples]

Samples

Input #1

2
12 5 1
6 1 0

Output #1

6
9

In the $1$\-st test case, the popcount of $1$ is $1$, the popcount of $6$ is $2$, and the popcount of $11$ is $3$, so $1+2+3=6$ should be printed.  
In the $2$\-nd test case, the popcount of $1$ is $1$, $2$ is $1$, $3$ is $2$, $4$ is $1$, $5$ is $2$, and $6$ is $2$, so $1+1+2+1+2+2=9$ should be printed.

API Response (JSON)

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  "problem": {
    "name": "Ex - Popcount Sum",
    "description": {
      "content": "Find the sum of popcounts of all integers between $1$ and $N$, inclusive, such that the remainder when divided by $M$ equals $R$.   Here, the popcount of a positive integer $X$ is the number of $1$s i",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 4000,
      "memory_limit": 262144
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    "difficulty": "None",
    "is_remote": true,
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    "sync_url": null,
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      "statement_type": "Markdown",
      "content": "Find the sum of popcounts of all integers between $1$ and $N$, inclusive, such that the remainder when divided by $M$ equals $R$.  \nHere, the popcount of a positive integer $X$ is the number of $1$s i...",
      "is_translate": false,
      "language": "English"
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