Z. Hard Compare
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

Given 4 numbers $$$A, B, C$$$ and $$$D$$$. If $$$A^B$$$ > $$$C^D$$$ print "YES" otherwise, print "NO".

Input

Only one line containing 4 numbers $$$A, B, C$$$ and $$$D$$$ $$$(1 \le A, C \le 10^7)$$$ , $$$(1 \le B, D \le 10^{12})$$$

Output

Print "YES" or "NO" according to the problem above.

Examples
Input
3 2 5 4
Output
NO
Input
5 2 4 2
Output
YES
Input
5 2 5 2
Output
NO
Note

First Example :

$$$3^2$$$ = 9 and $$$5^4$$$ = 625 then 9 < 625 so the answer is NO.

Second Example :

$$$5^2$$$ = 25 and $$$4^2$$$ = 16 then 25 > 16 so the answer is YES.

Third Example :

$$$5^2$$$ = 25 and $$$5^2$$$ = 25 then 25 = 25 so the answer is NO.