Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

The problem statement has recently been changed. View the changes.

×
C. Hacking Cypher

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputPolycarpus participates in a competition for hacking into a new secure messenger. He's almost won.

Having carefully studied the interaction protocol, Polycarpus came to the conclusion that the secret key can be obtained if he properly cuts the public key of the application into two parts. The public key is a long integer which may consist of even a million digits!

Polycarpus needs to find such a way to cut the public key into two nonempty parts, that the first (left) part is divisible by *a* as a separate number, and the second (right) part is divisible by *b* as a separate number. Both parts should be positive integers that have no leading zeros. Polycarpus knows values *a* and *b*.

Help Polycarpus and find any suitable method to cut the public key.

Input

The first line of the input contains the public key of the messenger — an integer without leading zeroes, its length is in range from 1 to 10^{6} digits. The second line contains a pair of space-separated positive integers *a*, *b* (1 ≤ *a*, *b* ≤ 10^{8}).

Output

In the first line print "YES" (without the quotes), if the method satisfying conditions above exists. In this case, next print two lines — the left and right parts after the cut. These two parts, being concatenated, must be exactly identical to the public key. The left part must be divisible by *a*, and the right part must be divisible by *b*. The two parts must be positive integers having no leading zeros. If there are several answers, print any of them.

If there is no answer, print in a single line "NO" (without the quotes).

Examples

Input

116401024

97 1024

Output

YES

11640

1024

Input

284254589153928171911281811000

1009 1000

Output

YES

2842545891539

28171911281811000

Input

120

12 1

Output

NO

Codeforces (c) Copyright 2010-2022 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: May/16/2022 22:44:51 (k2).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|