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This puzzle can be solved using the following concepts. Practice using these concepts and improve your skills.

Statement

 Goal

You're going back home late and unfortunately, you forgot your entry code. So you decide to try all the possibilities. It is not the smartest choice but your neighbors are sleeping...

The challenge is to find one of the shortest sequences of digits that contains all those possibilities.

There are x digits, from 0 to x-1, available for your entry code, and the code is composed of n of them.

For instance, there are eight possible codes for x = 2 and n = 3 : "000", "001", "010", "011", "100", "101", "110", and "111". And you can try all of them with the sequence "0001011100".

As there are multiple sequences of the same length that are solutions to this problem, you need to find the sequence describing the smallest possible number. For the previous example, the expected answer is not "0010111000" because 0010111000 > 0001011100.
Input
Line 1: The number x describing the available digits of the pad.
Line 2: The length n of your entry code.
Output
Line 1: The sequence to try all the codes.
Constraints
1 ≤ x ≤10
1 ≤ n <10
x^n < 1000
Example
Input
2
3
Output
0001011100

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