cf 18B

B. Platforms

time limit per test

2 seconds

memory limit per test

64 megabytes

input

standard input

output

standard output

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 dunits 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 test(s)

input

2 2 5 3

output

4

input

5 4 11 8

output

20

#include<iostream>
#include<cstdio>
#include<cstring>
#include<string>
#include<cmath>
#include<algorithm>
#include<cstdlib>
using namespace std;
#define LL long long
LL n,d,m,l;
int main()
{
      int i;
      scanf("%I64d%I64d%I64d%I64d",&n,&d,&m,&l);
      for(i=0;i<n-1;i++)
      {
          if((i*m+l)/d*d+d<(i+1)*m)
                  break;
      }
      printf("%I64d
",(i*m+l)/d*d+d);
      return 0;
}