LCM

AtCoder

IDarc200_b

Time2000ms

Memory256MB

Difficulty—

You are given positive integers $A_1,A_2,A_3$. Determine whether there exists a pair of positive integers $(X_1,X_2)$ that satisfies all the following conditions, and if it exists, find one. * $X_1$ is an integer with $A_1$ digits in decimal notation. * $X_2$ is an integer with $A_2$ digits in decimal notation. * The least common multiple of $X_1$ and $X_2$ is an integer with $A_3$ digits in decimal notation. You are given $T$ test cases, so find the answer for each. ## Constraints * $1\le T\le 17^3$ * $1\le A_1,A_2,A_3\le 17$ * All input values are integers. ## Input The input is given from Standard Input in the following format: $T$ $\text{case}_1$ $\text{case}_2$ $\vdots$ $\text{case}_T$ Each test case is given in the following format: $A_1$ $A_2$ $A_3$ [samples]

Samples

Input #1

Output #1

Yes
2025 200
No
Yes
20250615 200200

For the first test case, if we set $(X_1,X_2)=(2025,200)$, then the least common multiple of $X_1,X_2$ is $16200$, which satisfies the conditions. Other examples that satisfy the conditions include $(X_1,X_2)=(2025,125),(7777,231)$.

API Response (JSON)

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      "statement_type": "Markdown",
      "content": "You are given positive integers $A_1,A_2,A_3$.\nDetermine whether there exists a pair of positive integers $(X_1,X_2)$ that satisfies all the following conditions, and if it exists, find one.\n\n*   $X_1...",
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