E. Nika and turnip
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

Nika likes the fairy tale about the turnip. Everyone knows the fairy tale about the turnip, where they could pull it out of the ground with a common effort. A grandfather pulled a turnip, a grandmother pulled the grandfather, a granddaughter pulled the grandmother, Zhuchka pulled the granddaughter, a cat pulled Zhuchka, and a mouse pulled the cat. Nika is intrigued by the question: "Is the mouse really that strong?"

You know each of the $$$n$$$ helpers. An indicator of the strength of the $$$i$$$ helper is equal to $$$a_i$$$. Nika knows for sure that to pull out a turnip, you need to apply a minimum of $$$x$$$ force. The helpers can be swapped in any way in the row. When the helpers start pulling the turnip, their total strength equals $$$\displaystyle\sum_{i=1}^n\dfrac{b_i}{i}$$$, where $$$i$$$ is the number of the helper in the row (the first one stands furthest from the turnip, $$$n$$$ is holding onto the turnip), $$$b_i$$$ is his strength.

Help Nika determine if the helpers can pull out the turnip.

Input

The first line contains two integers $$$n$$$, $$$x$$$ $$$(1 \leq n \leq 1000, 1 \leq x \leq 10^{12})$$$  — the number of helpers and the total force that needs to be applied to pull the turnip out.

The second line contains $$$n$$$ integers $$$a_i$$$ $$$(1 \leq a_i \leq 10^{12})$$$  — the power of each helper.

Output

In a single line, print "YES" (without quotes) if the turnip can be pulled out, otherwise "NO".

Examples
Input
5 8
5 4 3 2 1
Output
YES
Input
6 20
10 4 2 4 2 8
Output
NO
Input
6 16
10 4 2 4 2 8
Output
YES