CF118D.Caesar's Legions

Gaius 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.

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.

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.

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