Battle

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.

Examples

Input

10 9 10 10

Output

No

Input

46 4 40 5

Output

Yes

inputFormat

input are integers.

Input

Input is given from Standard Input in the following format:

A B C D

outputFormat

Output

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

Examples

Input

10 9 10 10

Output

No

Input

46 4 40 5

Output

Yes

样例

46 4 40 5

Yes