Dragon's Question

Time limit3sMemory limit256 MB

Problem

In a faraway land there lives a nobleman who has three sons. The eldest is very clever; his special strength is calculation, and he can work out a fifth-order determinant in his head, with no paper or pencil. The middle brother is also very talented, particularly strong in theoretical questions. But the youngest brother has no talent for mathematics at all.

One day the three of them went for a walk. Suddenly the wind began to blow and something blotted out the sun: it was a hungry dragon returning to its lair from an unsuccessful hunt.

"Hey, boys! I will give you a problem, and if you cannot solve it, nothing will save you!" said the dragon.

The elder brothers only smiled: surely no dragon could ask a question they could not answer.

"Give me a positive integer that is divisible by $d$ and has exactly $n$ digits, taking $d$ equal to forty-five and $n$ equal to three!" was the dragon's question.

"One hundred thirty-five," answered the eldest brother.

"Good, go where you like. But I will return in a year and ask you a similar question," said the disappointed dragon, and flew away.

A year passed; the eldest brother married and left his parents' home. The two younger brothers went for a walk, discussing the event, and met the dragon again.

"Hey, boys, give me a positive integer that is divisible by twenty-three and has exactly one digit," asked the dragon.

"No solution," answered the middle brother.

"You are still too clever, go where you like. But I will return and ask again," said the dragon, and flew away.

Another year passed; the middle brother married and left home. Now the youngest brother never goes outside, because he does not have enough knowledge to answer the dragon's questions. Please help him and write a program, for the boy is very afraid.

Given $n$ and $d$, find the smallest positive integer that has exactly $n$ digits (with no leading zeros) and is divisible by $d$. If no such number exists, report that there is no solution.

Input

A single line contains two integers $n$ and $d$ ($1 \le n \le 1000$; $1 \le d \le 10^6$).

Output

Print a single line: the smallest $n$-digit positive integer (without leading zeros) that is divisible by $d$, or the string No solution if no such number exists.