2287번 - 모노디지털 표현 다국어

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2 초 128 MB127443624431.647%

문제

몇 개의 숫자 K(K는 1, 2, …, 9중 하나)와 사칙 연산(덧셈, 뺄셈, 곱셈, 나눗셈)만을 사용하여 어떤 자연수 X를 수식으로 표현한 것을 X의 K-표현이라 부른다. 수식에는 괄호가 포함될 수 있으며, 나눗셈은 나눈 몫만을 취한다.

예를 들어 12의 5-표현을 몇 개 써 보면 5+5+(5/5)+(5/5), 55/5+5/5, (55+5)/5 등이 있다. K-표현의 길이를 사용한 K의 개수라 하면, 각각의 길이는 6, 5, 4가 된다.

K가 주어졌을 때, 어떤 자연수의 K-표현 중 가장 짧은 길이를 알아보려 한다.

입력

첫째 줄에 K가 주어진다. 다음 줄에는 표현 식을 찾을 수의 개수 n(1 ≤ n ≤ 1,000)이 주어진다. 다음 줄에는 K-표현 중 가장 짧은 길이를 알아보려 하는 자연수 a(1 ≤ a ≤ 32,000)가 주어진다.

출력

입력되는 순서대로 K-표현의 최소 길이를 n개의 줄에 출력한다. 만약 K-표현의 최소 길이가 8보다 크다면 “NO"를 출력한다.

예제 입력 1 

5
2
12
31168

예제 출력 1 

4
NO
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