[GDCPC 2023] X Equals Y

Luogu

IDLGP9699

Time3000ms

Memory1024MB

DifficultyP5

数学2023广东Special JudgeO2优化进制省赛/邀请赛

For positive integers $X$ and $b \geq 2$, define $f(X,b)$ as a sequence which describes the base-$b$ representation of $X$, where the $i$-th element in the sequence is the $i$-th least significant digit in the base-$b$ representation of $X$. For example, $f(6, 2) = \{0, 1, 1\}$, while $f(233, 17) = \{12, 13\}$. Given four positive integers $x$, $y$, $A$ and $B$, please find two positive integers $a$ and $b$ satisfying: - $2 \leq a \leq A$ - $2 \leq b \leq B$ - $f(x, a) = f(y, b)$ ## Input There are multiple test cases. The first line of the input contains an integer $T$ ($1 \leq T \leq 10^3$) indicating the number of test cases. For each test case: The first line contains four integers $x$, $y$, $A$ and $B$ ($1 \leq x,y \leq 10^9$, $2 \leq A,B \leq 10^9$). It's guaranteed that there are at most $50$ test cases satisfying $\max(x, y) > 10^6$. ## Output For each test case, if valid positive integers $a$ and $b$ do not exist, output $\texttt{NO}$ in one line. Otherwise, first output $\texttt{YES}$ in one line. Then in the next line, output two integers $a$ and $b$ separated by a space. If there are multiple valid answers, you can output any of them. [samples]

Samples

Input #1

6
1 1 1000 1000
1 2 1000 1000
3 11 1000 1000
157 291 5 6
157 291 3 6
10126 114514 789 12345

Output #1

YES
2 2
NO
YES
2 10
YES
4 5
NO
YES
779 9478

API Response (JSON)

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  "problem": {
    "name": "[GDCPC 2023] X Equals Y",
    "description": {
      "content": "For positive integers $X$ and $b \\geq 2$, define $f(X,b)$ as a sequence which describes the base-$b$ representation of $X$, where the $i$-th element in the sequence is the $i$-th least significant dig",
      "description_type": "Markdown"
    },
    "platform": "Luogu",
    "limit": {
      "time_limit": 3000,
      "memory_limit": 1048576
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    "difficulty": {
      "LuoguStyle": "P5"
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    "is_remote": true,
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    "sync_url": null,
    "sign": "LGP9699"
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  "statements": [
    {
      "statement_type": "Markdown",
      "content": "For positive integers $X$ and $b \\geq 2$, define $f(X,b)$ as a sequence which describes the base-$b$ representation of $X$, where the $i$-th element in the sequence is the $i$-th least significant dig...",
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      "language": "English"
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