USACO 2012 February Contest, Silver Division

Problem 2. Cow IDs

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Problem 2: Cow IDs [Brian Dean, 2012] Being a secret computer geek, Farmer John labels all of his cows with binary numbers. However, he is a bit superstitious, and only labels cows with binary numbers that have exactly K "1" bits (1 <= K <= 10). The leading bit of each label is always a "1" bit, of course. FJ assigns labels in increasing numeric order, starting from the smallest possible valid label -- a K-bit number consisting of all "1" bits. Unfortunately, he loses track of his labeling and needs your help: please determine the Nth label he should assign (1 <= N <= 10^7). PROBLEM NAME: cowids INPUT FORMAT: * Line 1: Two space-separated integers, N and K. SAMPLE INPUT (file 7 3 INPUT DETAILS: Among all binary numbers containing exactly 3 "1" bits, FJ wants to output the 7th in increasing sorted order. SAMPLE OUTPUT (file cowids.out): 10110
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