B. Starving
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

You're in a field, which can be represented by $$$n + 1$$$ cells numbered from $$$0$$$ to $$$n$$$. The state of the field can be represented by a sequence of $$$n$$$ integers $$$a_1, a_2, ..., a_n$$$. For all $$$i$$$, if $$$a_i \gt 0$$$, then cell $$$i$$$ contains a watermelon worth $$$a_i$$$ health. Otherwise, if $$$a_i = 0$$$, then cell $$$i$$$ is empty. Cell $$$0$$$ is always empty. Initially, you're located in cell $$$0$$$ and have $$$h$$$ health.

In each minute, the following will occur in order:

  • Suppose you're in cell $$$i$$$. If $$$i \lt n$$$, you have the option to move to cell $$$i + 1$$$. If $$$i \gt 0$$$, you have the option to move to cell $$$i - 1$$$. You must pick an option. Let $$$j$$$ be the new cell you move to.
  • If cell $$$j$$$ contains a watermelon, you eat it and $$$h$$$ increases by $$$a_j$$$. The watermelon disappears and $$$a_j$$$ becomes $$$0$$$.
  • $$$h$$$ decreases by $$$1$$$. If $$$h = 0$$$, then you starve.
  • The health value of all uneaten watermelons increases by $$$1$$$. In other words, for all $$$k$$$ such that $$$a_k \gt 0$$$, $$$a_k$$$ increases by $$$1$$$.

Please determine if it's possible for you to reach cell $$$n$$$ without starving. It doesn't count if you starve in the last minute.

Input

The first line of input consists of two space-separated integers $$$n$$$ and $$$h$$$ $$$(1 \leq n, h \leq 2 \cdot 10^5)$$$.

The second line of input consists of $$$n$$$ space-separated integers $$$a_1, a_2, ..., a_n$$$ $$$(0 \leq a_i \leq 2 \cdot 10^5)$$$.

Output

On the first and only line, output YES if it's possible for you to reach cell $$$n$$$ without starving. Otherwise, output NO.

Examples
Input
10 3
1 1 1 0 0 0 0 0 0 0
Output
YES
Input
11 3
1 1 1 0 0 0 0 0 0 0 0
Output
NO
Input
1 1
1
Output
YES
Note

One possible path to cell $$$n$$$ for the first sample test case looks like this:

It can be proven that it is impossible to reach cell $$$n$$$ without starving in the second test case.