codeforce 18B

http://vjudge.net/contest/view.action?cid=48098#problem/B

Description

In one one-dimensional world there are n platforms. Platform with index k (platforms are numbered from 1) is a segment with coordinates [(k - 1)m, (k - 1)m + l], and l < m. Grasshopper Bob starts to jump along the platforms from point 0, with each jump he moves exactly d units right. Find out the coordinate of the point, where Bob will fall down. The grasshopper falls down, if he finds himself not on the platform, but if he finds himself on the edge of the platform, he doesn't fall down.

Input

The first input line contains 4 integer numbers n, d, m, l (1 ≤ n, d, m, l ≤ 10⁶, l < m) — respectively: amount of platforms, length of the grasshopper Bob's jump, and numbers m and l needed to find coordinates of the k-th platform: [(k - 1)m, (k - 1)m + l].

Output

Output the coordinates of the point, where the grosshopper will fall down. Don't forget that if Bob finds himself on the platform edge, he doesn't fall down.

Sample Input

Input

2 2 5 3

Output

4

Input

5 4 11 8

Output

20

题目大意：在x轴上有n块地板，从原点开始排列，每块地板所占据的坐标区间为[(m-1)*k,(m-1)*k+l]  (注意这里是闭区间，因此边缘点也在地板上)。一个人从原点开始跳跃，每次跳跃的距离为d，求这个人第一次落下的点不在地板上的坐标。

#include<stdio.h>
long long  n,d,m,l,i=1,t;
int main()
{
    while(~scanf("%lld%lld%lld%lld",&n,&d,&m,&l))
    {
        for(i=0; i<n-1; i++)
            if((i*m+l)/d*d+d<(i+1)*m)
                 break;
        printf("%lld\n",(i*m+l)/d*d+d);
    }
    return 0;
}