Vasya and Digital Root

题意翻译

- 现有一个函数 $S(n)$ 表示 $n$ 各个数位之和； - 又有 $dr(n)$ 满足： - $S(n)<10 \rightarrow dr(n)=S(n)$ - $S(n)\ge 10\rightarrow dr(n)=dr(S(n))$ - 给定 $k$,$d$， 求一个 $k$ 位数 $n$ 满足： - $dr(n)=d$ - 若没有数满足条件，请输出 `No solution`。 ### 数据范围 $1 \leq k \leq 1000$，$0 \leq d \leq 9$。

题目描述

Vasya has recently found out what a digital root of a number is and he decided to share his knowledge with you. Let's assume that $ S(n) $ is the sum of digits of number $ n $ , for example, $ S(4098)=4+0+9+8=21 $ . Then the digital root of number $ n $ equals to: 1. $ dr(n)=S(n) $ , if $ S(n)&lt;10 $ ; 2. $ dr(n)=dr(S(n)) $ , if $ S(n)>=10 $ . For example, $ dr(4098)=dr(21)=3 $ . Vasya is afraid of large numbers, so the numbers he works with are at most $ 10^{1000} $ . For all such numbers, he has proved that $ dr(n)=S(S(S(S(n)))) $ $ (n<=10^{1000}) $ . Now Vasya wants to quickly find numbers with the given digital root. The problem is, he hasn't learned how to do that and he asked you to help him. You task is, given numbers $ k $ and $ d $ , find the number consisting of exactly $ k $ digits (the leading zeroes are not allowed), with digital root equal to $ d $ , or else state that such number does not exist.

输入输出格式

输入格式

The first line contains two integers $ k $ and $ d $ $ (1<=k<=1000; 0<=d<=9) $ .

输出格式

In a single line print either any number that meets the requirements (without the leading zeroes) or "No solution" (without the quotes), if the corresponding number does not exist. The chosen number must consist of exactly $ k $ digits. We assume that number 0 doesn't contain any leading zeroes.

输入输出样例

输入样例 #1

4 4

输出样例 #1

5881

输入样例 #2

5 1

输出样例 #2

36172

输入样例 #3

1 0

输出样例 #3

0

说明

For the first test sample $ dr(5881)=dr(22)=4 $ . For the second test sample $ dr(36172)=dr(19)=dr(10)=1 $ .