Determine for each positive integer $n$ in the interval $[L, R]$ whether it can be the area of a right-angled triangle with rational side lengths.

Input

A single line containing two positive integers $L$ and $R$.

Output

A string consisting of $0$s and $1$s, representing whether it is possible for each integer in the range $[L, R]$ respectively.

Examples

Input 1

1 6

Output 1

000011

Note 1

Only $5$ and $6$ satisfy the condition. $5$ is the area of a right-angled triangle with side lengths $\frac{20}{3}, \frac{3}{2}, \frac{41}{6}$. $6$ is the area of a right-angled triangle with side lengths $3, 4, 5$.

Constraints

For $30\%$ of the data, $1 \leqslant L \leqslant R \leqslant 10$.

For $50\%$ of the data, $1 \leqslant L \leqslant R \leqslant 100$.

Additionally, for $20\%$ of the data, $R - L \leqslant 3$.

For $100\%$ of the data, $1 \leqslant L \leqslant R \leqslant 5 \times 10^5$.