Lost Bits

Kostya has a fondness for all natural numbers, but he especially loves those he considers beautiful. A number is deemed beautiful if it is divisible by k.

One day, Kostya encountered a beautiful natural number, n, while shopping. He was so taken with it that he decided to purchase it as a gift for his mother. However, upon returning home, he discovered that some bits of the number had somehow been lost, turning it into an unbeautiful number, m. Your task is to help Kostya restore some bits so that the number becomes beautiful again. (Restoring a bit involves changing a bit from 0 to 1.)

Input

The first line contains two integers: m and k, both less than or equal to $10^6$.

Output

Print the number n on a single line. If there are multiple possibilities, print the smallest possible option. If it is impossible to make the number beautiful, print -1.

Examples

Note

Consider the first example where m=4, which is represented in binary as 100. There are three potential ways to restore the bits:

• Restore the least significant bit, resulting in 101[2] = 5[10], which is not divisible by 3.

• Restore the middle bit, resulting in 110[2] = 6[10], which is divisible by 3.

• Restore both the least significant and middle bits, resulting in 111[2] = 7[10], which is not divisible by 3.

Therefore, the only valid solution is the number 6.