Little A provides three integers $n, m, k$ such that $0 \le k \le m < n$. He wants Little B to construct a binary string of length $n$.

Little B says, "Is that all?", and writes down $n$ ones. Clearly, this string satisfies the conditions.

Little A does not want too many ones, so he requires that every substring of length $m$ in the binary string contains at most $k$ ones.

Little B says, "Is that all?", and writes down $n$ zeros. Clearly, this string also satisfies the conditions.

Little A also does not want too few ones, so he further requires that every substring of length $m+1$ in the binary string contains at least $k$ ones.

You say, "Is that all?", and you also want to write down a string that satisfies all of Little A's conditions.

In this problem, $T$ is a substring of $S$ if and only if $T$ is formed by removing some (possibly zero) characters from the beginning or the end of $S$.

Input

A single line containing three integers $n, m, k$.

Output

A single line containing a binary string of length $n$. If there are multiple strings that satisfy the conditions, you may output any one of them.

Examples

Input 1

4 2 1

Output 1

0100

Note 1

The string 0100 has $3$ substrings of length $m$, which are 01, 10, and 00. Each of these contains $\le k$ ones.

The string 0100 has $2$ substrings of length $m+1$, which are 010 and 100. Each of these contains $\ge k$ ones.

Therefore, 0100 satisfies the conditions.

Note that there is more than one valid string; for example, 0010 also satisfies the conditions, so outputting 0010 is also correct.

Input 2

5 4 4

Output 2

11111

Constraints

There are $10$ test cases in this problem, each worth $10$ points.

For all test cases, it is guaranteed that $0 \le k \le m < n \le 10^5$ and $0 < m$.

For test cases $1$ and $2$, $n \le 20$.

For test cases $3$ and $4$, $n \le 100$.

For test cases $5$ and $6$, $n \le 1000$.

For test case $7$, $k = m$.

For test case $8$, $m = n - 1$.

For test cases $9$ and $10$, there are no special restrictions.