Simple Math 4

AtCoder

IDarc176_b

Time2000ms

Memory256MB

Difficulty—

Find the last digit of the remainder when $2^N$ is divided by $2^M - 2^K$. You are given $T$ test cases, each of which must be solved. ## Constraints * $1 \le T \le 2 \times 10^5$ * $1 \le N \le 10^{18}$ * $1 \le K < M \le 10^{18}$ * $N,M,K$ are integers. ## Input The input is given from Standard Input in the following format, where $\mathrm{case}_i$ represents the $i$\-th test case: $T$ $\mathrm{case}_1$ $\mathrm{case}_2$ $\vdots$ $\mathrm{case}_T$ Each test case is given in the following format: $N$ $M$ $K$ [samples]

Samples

Input #1

5
9 6 2
123 84 50
95 127 79
1000000007 998244353 924844033
473234053352300580 254411431220543632 62658522328486675

Output #1

2
8
8
8
4

For the first test case, the remainder of $2^9$ divided by $2^6 - 2^2$ is $32$. Thus, the answer is the last digit of $32$, which is $2$.

API Response (JSON)

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      "statement_type": "Markdown",
      "content": "Find the last digit of the remainder when $2^N$ is divided by $2^M - 2^K$.\nYou are given $T$ test cases, each of which must be solved.\n\n## Constraints\n\n*   $1 \\le T \\le 2 \\times 10^5$\n*   $1 \\le N \\le...",
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