Description

有M个未各数X1,X2....Xm,求满足以下条件不等式的 正整数解 1：1<=i<=N,Xi<=t 2:X1+X2+...+Xm<=s

Format

Input

一行四个数S,T,N,M

S<=10^18,N<=10^9,N*T<=S，m-n<=1000

Output

输出方案数Mod 10^9+7

Samples

5 2 2 3

8