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The 1999 British Informatics Olympiad Final
Zig-zag numbers

A zig-zag number is one where the digits alternatively rise and fall, always rising initially. For example, there are sixteen zig-zag numbers using the digits 1,...,5:

13254   15342   25143   35142
14253   23154   25341   35241
14352   24153   34152   45132
15243   24351   34251   45231

Write a program that inputs two numbers : b (1<=b<=15) then n. You should calculate the nth zig-zag number (in increasing numerical order) that uses the digits 1,...,b once each. If there are Zb such zig-zag numbers, you will always be given 1<=n<=Zb. Z15 fits into a signed 32-bit integer.

Sample Input 1

5 10

Sample Output 1


Sample Input 2

15 50000000

Sample Output 2


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