{"problem":{"name":"[信息与未来 2018] 整数乘方","description":{"content":"定义 $a$ 的 $n$ 次幂 $a^n = a × a × \\cdots × a$（共 $n$ 个 $a$ 相乘）。记 $a^n$ 的十进制表示转换为字符串后奇数字符（阿拉伯数字 $1, 3, 5, 7, 9$）的个数为 $A$，偶数字符（阿拉伯数字 $0, 2, 4, 6, 8$）的个数为 $B$，求 $A-B$ 的数值。 例如，$a = 3, n = 12, a^n = 3^{12} = ","description_type":"Markdown"},"platform":"Luogu","limit":{"time_limit":1000,"memory_limit":131072},"difficulty":{"LuoguStyle":"P3"},"is_remote":true,"is_sync":true,"sync_url":null,"sign":"LGB3739"},"statements":[{"statement_type":"Markdown","content":"定义 $a$ 的 $n$ 次幂 $a^n = a × a × \\cdots × a$（共 $n$ 个 $a$ 相乘）。记 $a^n$ 的十进制表示转换为字符串后奇数字符（阿拉伯数字 $1, 3, 5, 7, 9$）的个数为 $A$，偶数字符（阿拉伯数字 $0, 2, 4, 6, 8$）的个数为 $B$，求 $A-B$ 的数值。\n\n例如，$a = 3, n = 12, a^n = 3^{12} = (531441)_{10}$。\n\n奇数数位用方框标出：$\\boxed{5}\\boxed{3}\\boxed{1}44\\boxed{1}$，故 $A = 4$；\n\n偶数数位用方框标出：$531\\boxed{4}\\boxed{4}1$, 故 $B = 2, A-B = 2$。\n\n## Input\n\n输入一行两个整数 $a, n$。\n\n## Output\n\n输出一行一个整数，代表 $A − B$ 的值。\n\n[samples]\n\n## Note\n\n### 样例 $2$ 解释\n$5^{18} = 3814697265625，A - B = −1$。\n### 数据规模\n$30\\%$ 的数据满足 $a^n < 2^{32}$；\n\n所有数据满足 $2 ≤ a ≤ 9, 1 ≤ n ≤ 100$。\n> 本题原始满分为 $20\\text{pts}$。","is_translate":false,"language":"English"}],"meta":{"iden":"LGB3739","tags":["模拟","高精度","2018","江苏","信息与未来"],"sample_group":[["3 12","2"],["5 18","-1"]],"created_at":"2026-03-03 11:09:25"}}