{"problem":{"name":"LCM","description":{"content":"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","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"arc200_b"},"statements":[{"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*   $X_1$ is an integer with $A_1$ digits in decimal notation.\n*   $X_2$ is an integer with $A_2$ digits in decimal notation.\n*   The least common multiple of $X_1$ and $X_2$ is an integer with $A_3$ digits in decimal notation.\n\nYou are given $T$ test cases, so find the answer for each.\n\n## Constraints\n\n*   $1\\le T\\le 17^3$\n*   $1\\le A_1,A_2,A_3\\le 17$\n*   All input values are integers.\n\n## Input\n\nThe input is given from Standard Input in the following format:\n\n$T$\n$\\text{case}_1$\n$\\text{case}_2$\n$\\vdots$\n$\\text{case}_T$\n\nEach test case is given in the following format:\n\n$A_1$ $A_2$ $A_3$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"arc200_b","tags":[],"sample_group":[["3\n4 3 5\n1 1 7\n8 6 11","Yes\n2025 200\nNo\nYes\n20250615 200200\n\nFor 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 $(X_1,X_2)=(2025,125),(7777,231)$."]],"created_at":"2026-03-03 11:01:14"}}