Problem:
Score : 200 points

Problem Statement

Takahashi and Aoki will have a battle using their monsters.

The health and strength of Takahashi's monster are A and B, respectively, and those of Aoki's monster are C and D, respectively.

The two monsters will take turns attacking, in the order Takahashi's, Aoki's, Takahashi's, Aoki's, ...
Here, an attack decreases the opponent's health by the value equal to the attacker's strength.
The monsters keep attacking until the health of one monster becomes 0 or below. The person with the monster whose health becomes 0 or below loses, and the other person wins.

If Takahashi will win, print Yes; if he will lose, print No.

Constraints

1 \leq A,B,C,D \leq 100

All values in input are integers.

Input

Input is given from Standard Input in the following format:

A B C D

Output

If Takahashi will win, print Yes; if he will lose, print No.

Sample Input 1

10 9 10 10

Sample Output 1

No

First, Takahashi's monster attacks Aoki's monster, whose health is now 10-9=1.

Next, Aoki's monster attacks Takahashi's monster, whose health is now 10-10=0.

Takahashi's monster is the first to have 0 or less health, so Takahashi loses.

Sample Input 2

46 4 40 5

Sample Output 2

Yes

Solution in JavaScript (Node.js 12.16.1) (judge verdict: Wrong Answer)


function Main (input) {
  var t_life = parseInt(input.split(" ")[0]);
  var t_atk = parseInt(input.split(" ")[1]);
  var a_life = parseInt(input.split(" ")[2]);
  var a_atk = parseInt(input.split(" ")[3]);
  
  for (var counter = 0; counter < 100; counter++) {
    if (counter % 2 === 0) {
        // 高橋君の番
        a_life = a_life - t_atk
        if (a_life <= 0) {
        console.log("Yes")
        }
    } else {
        // 青木君の番
        t_life = t_life - a_atk
        if (t_life <= 0) {
        console.log("Yes")
        }
    }
  }
}

Main(require("fs").readFileSync("/dev/stdin", "utf8"));