Ternary Decomposition

AtCoder

IDarc164_a

Time2000ms

Memory256MB

Difficulty—

You are given integers $N$ and $K$. Is it possible to express $N$ as the sum of exactly $K$ numbers of the form $3^m$ ($m$ is a non-negative integer)? In other words, is there a sequence of non-negative integers $(m_1, m_2,\ldots, m_K)$ such that: $N= 3^{m_1}+3^{m_2}+...+3^{m_K}$? You are given $T$ test cases. Answer each of them. ## Constraints * $1 \leq T \leq 10^5$ * $1 \leq K \leq N \leq 10^{18}$ * All input values are integers. ## Input The input is given from Standard Input in the following format: $T$ $\mathrm{case}_1$ $\mathrm{case}_2$ $\vdots$ $\mathrm{case}_T$ Each test case, $\mathrm{case}_i (1\leq i \leq T)$, is in the following format: $N$ $K$ [samples]

Samples

Input #1

4
5 3
17 2
163 79
1000000000000000000 1000000000000000000

Output #1

Yes
No
Yes
Yes

For the first test case, we have $5=3^1+3^0+3^0$, so the condition in question is satisfied.
For the second test case, there is no sequence of non-negative integers $(m_1, m_2)$ such that $17=3^{m_1}+3^{m_2}$, so the condition in question is not satisfied.

API Response (JSON)

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