class Solution {

public:

    int kthGrammar(int N, int K) {

        return helper(N, K, false);

    }

    int helper(int n, int k, bool reverse) {

        if (n == ) return reverse;

        int total =  << (n-);

        int half = total >> ;

        if (k <= half)

            return helper(n-, k, reverse);

        else

            return helper(n-, k-half, !reverse);

    }

};

/*

lvl1: 0

lvl2: 0 1

lvl3: 0 1 1 0

lvl4: 0 1 1 0   1 0 0 1

lvl5: 0 1 1 0   1 0 0 1   1 0 0 1   0 1 1 0

      0 1 1 0   1 0 0 1   1 0 0 1   0 1 1 0   1 0 0 1   0 1 1 0   0 1 1 0   1 0 0 1

      */