题干：

In some game by Playrix it takes t minutes for an oven to bake k carrot cakes, all cakes are ready at the same moment t minutes after they started baking. Arkady needs at least n cakes to complete a task, but he currently don't have any. However, he has infinitely many ingredients and one oven. Moreover, Arkady can build one more similar oven to make the process faster, it would take d minutes to build the oven. While the new oven is being built, only old one can bake cakes, after the new oven is built, both ovens bake simultaneously. Arkady can't build more than one oven.

Determine if it is reasonable to build the second oven, i.e. will it decrease the minimum time needed to get n cakes or not. If the time needed with the second oven is the same as with one oven, then it is unreasonable.

Input

The only line contains four integers n, t, k, d (1 ≤ n, t, k, d ≤ 1 000) — the number of cakes needed, the time needed for one oven to bake k cakes, the number of cakes baked at the same time, the time needed to build the second oven.

Output

If it is reasonable to build the second oven, print "YES". Otherwise print "NO".

Examples

Input

8 6 4 5

Output

YES

Input

8 6 4 6

Output

NO

Input

10 3 11 4

Output

NO

Input

4 2 1 4

Output

YES

Note

In the first example it is possible to get 8 cakes in 12 minutes using one oven. The second oven can be built in 5 minutes, so after 6 minutes the first oven bakes 4cakes, the second oven bakes 4 more ovens after 11 minutes. Thus, it is reasonable to build the second oven.

In the second example it doesn't matter whether we build the second oven or not, thus it takes 12 minutes to bake 8 cakes in both cases. Thus, it is unreasonable to build the second oven.

In the third example the first oven bakes 11 cakes in 3 minutes, that is more than needed 10. It is unreasonable to build the second oven, because its building takes more time that baking the needed number of cakes using the only oven.

 

题目大意：

烤k个饼干需要t秒，她们要至少烤制n块饼干。第一个炉子已经预热好了，但是第二个炉子没有。第二个炉子预热需要d秒。k个饼干在t秒同时烤好，第二个炉子在预热的时候只能用第一个炉子，第二个炉子预热结束之后，两个炉子可以同时用。请你帮帮她判断应不应该用第二个炉子，在速度一样快的时候她们嫌麻烦不去预热第二个炉子（If the time needed with the second oven is the same as with one oven, then it is unreasonable.如果预热第二个炉子总共花的时间和不预热一样，则认为不预热第二个炉子），她们会选择最快的一种方案。

解题报告：

  先计算出一共要弄多少锅（假设需要all锅），然后看看all-1锅的时间是否大于预热的时间，如果严格大于预热的时间我就可以在第一锅弄着的时候，开一个第二锅，时间一定短，输出YES 否则就是NO。有个细节就是，这里需要严格大于！因为等于的意思是，我all-1锅都好了（也就是，只差一锅了），所以我开第二锅和不开第二锅都一样的总时长了，所以依据题意，此时输出NO。

AC代码：

#include <bits/stdc++.h>
using namespace std;
int n,t,k,d;
int main()
{
    cin>>n>>t>>k>>d;
    if (k>=n) return 0*puts("NO");//神操作。 
    int guo=(n%k==0)?n/k:n/k+1;
    if ((guo-1)*t>d) return 0*puts("YES");
    return 0*puts("NO");
}