Package for this problem was not updated by the problem writer or Codeforces administration after we’ve upgraded the judging servers. To adjust the time limit constraint, solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then value 800 ms will be displayed and used to determine the verdict.

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ACM-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

D. Caesar's Legions

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputGaius Julius Caesar, a famous general, loved to line up his soldiers. Overall the army had *n*_{1} footmen and *n*_{2} horsemen. Caesar thought that an arrangement is not beautiful if somewhere in the line there are strictly more that *k*_{1} footmen standing successively one after another, or there are strictly more than *k*_{2} horsemen standing successively one after another. Find the number of beautiful arrangements of the soldiers.

Note that all *n*_{1} + *n*_{2} warriors should be present at each arrangement. All footmen are considered indistinguishable among themselves. Similarly, all horsemen are considered indistinguishable among themselves.

Input

The only line contains four space-separated integers *n*_{1}, *n*_{2}, *k*_{1}, *k*_{2} (1 ≤ *n*_{1}, *n*_{2} ≤ 100, 1 ≤ *k*_{1}, *k*_{2} ≤ 10) which represent how many footmen and horsemen there are and the largest acceptable number of footmen and horsemen standing in succession, correspondingly.

Output

Print the number of beautiful arrangements of the army modulo 100000000 (10^{8}). That is, print the number of such ways to line up the soldiers, that no more than *k*_{1} footmen stand successively, and no more than *k*_{2} horsemen stand successively.

Examples

Input

2 1 1 10

Output

1

Input

2 3 1 2

Output

5

Input

2 4 1 1

Output

0

Note

Let's mark a footman as 1, and a horseman as 2.

In the first sample the only beautiful line-up is: 121

In the second sample 5 beautiful line-ups exist: 12122, 12212, 21212, 21221, 22121

Codeforces (c) Copyright 2010-2017 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Jun/25/2017 15:14:23 (c3).

Desktop version, switch to mobile version.

User lists

Name |
---|