Given some number of ones and zeros, numOnes and numZeros respectively, find the nth permutation of the vector [ones(1,numOnes), zeros(1,numZeros)] according to the lexicographical order. For example, if numOnes = 3 and numZeros = 2 then there are nchoosek(5,3) = 10 permutations of 11100. The lexicographic numbering is below
1 11100
2 11010
3 11001
4 10110
5 10101
6 10011
7 01110
8 01101
9 01011
10 00111
so for instance nthPerm(3,2,8) = [0,1,1,0,1]. You can assume that numOnes and numZeros will always be greater than or equal to 1. Lastly, your code should not enumerate all possibilities since one of the test cases contains billions of permutations.
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William Chris Cleveland George Berken Ramon Villamangca

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