Resonant Vault Codes

Deep beneath an old observatory, engineers labeled every sealed vault door with a numeric code. A code is called resonant if none of its digits is zero and the code itself is evenly divisible by every one of its own digits. For example, 128 is resonant because 128 is divisible by 1, 2, and 8, while 23 is not resonant because 23 is not evenly divisible by 2, and 105 is not resonant because it contains a zero digit.

You are given two integers low and high describing an inclusive range of vault codes installed on the doors of a wing under inspection. Report every resonant code within that range, in increasing order, so the inspection team knows which doors will unlock correctly.

Input format

A single line containing two integers low and high.

Output format

Print all resonant codes in the range [low, high], inclusive, in increasing order, separated by single spaces on one line. If no resonant code exists in the range, print an empty line.

Constraints

• 1 <= low <= high <= 10000

1 22

1 2 3 4 5 6 7 8 9 11 12 15 22

47 85

48 55 66 77