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.

著名将领盖乌斯·尤利乌斯·凯撒热衷于排列他的士兵。整支军队共有 $n_1$ 名步兵和 $n_2$ 名骑兵。凯撒认为，若在队列中某处连续出现严格多于 $k_1$ 名步兵，或连续出现严格多于 $k_2$ 名骑兵，则该排列不美观。求所有美观的士兵排列数目。

注意：每种排列都必须包含全部 $n_1 + n_2$ 名战士。所有步兵彼此不可区分；同理，所有骑兵也彼此不可区分。

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.

唯一的一行包含四个以空格分隔的整数 $n_1$、$n_2$、$k_1$、$k_2$（$1 ≤ n_1, n_2 ≤ 100$，$1 ≤ k_1, k_2 ≤ 10$），分别表示步兵和骑兵的数量，以及允许连续站立的最大步兵数和最大骑兵数。

Print the number of beautiful arrangements of the army modulo 100000000 (108). 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.

输出军队的优美排列数对 $100000000$（即 $10^8$）取模的结果。也就是说，输出满足以下条件的士兵排队方式数目：至多有 $k_1$ 个步兵连续排列，且至多有 $k_2$ 个骑兵连续排列。

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

我们将步兵标记为 1，骑兵标记为 2。

在第一个样例中，唯一的优美队列为：121

在第二个样例中，存在 5 种优美队列：12122、12212、21212、21221、22121