You are given a set S of strings consisting of 0 and 1, and an integer K.

Find the longest string that is a subsequence of K or more different strings in S. If there are multiple strings that satisfy this condition, find the lexicographically smallest such string.

Here, S is given in the format below:

• The data directly given to you is an integer N, and N+1 strings X_0,X_1,...,X_N. For every $i (0\leq i\leq N)$, the length of X_i is 2^i.
• For every pair of two integers $(i,j) (0\leq i\leq N,0\leq j\leq 2^i-1)$, the j-th character of X_i is 1 if and only if the binary representation of j with i digits (possibly with leading zeros) belongs to S. Here, the first and last characters in X_i are called the 0-th and (2^i-1)-th characters, respectively.
• S does not contain a string with length N+1 or more.

Here, a string A is a subsequence of another string B when there exists a sequence of integers t_1 < ... < t_{|A|} such that, for every $i (1\leq i\leq |A|)$, the i-th character of A and the t_i-th character of B is equal.

Constraints

• $0 \leq N \leq 20$
• $X_i(0\leq i\leq N)$ is a string of length 2^i consisting of 0 and 1.
• $1 \leq K \leq |S|$
• K is an integer.

Input

Input is given from Standard Input in the following format:

N K
X_0
:
X_N

Output

Print the lexicographically smallest string among the longest strings that are subsequences of K or more different strings in S.

Examples

Input

3 4
1
01
1011
01001110

Output

10

Input

4 6
1
01
1011
10111010
1101110011111101

Output

100

Input

2 5
0
11
1111

Output

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