Irritable Bowel Syndrome

Time limit2sMemory limit1024 MB

Summary

Given daily stress changes where positive values add stress and negative values relieve it down to 0, count the days the accumulated stress is at least M.

Level: Easy2 of 10
Topics: Simulation, Implementation
Solved: No attempts yet

Problem

Sangwon has irritable bowel syndrome. The cause of irritable bowel syndrome is stress!

The daily stress changes over $N$ days are given as $A_1,\cdots ,A_N$ . If $A_i \ge 0$ , then $A_i$ units of stress build up on day $i$ . If $A_i < 0$ , then $-A_i$ units of stress are relieved on day $i$ . The stress level is $0$ when observation begins. If the amount of stress relieved is greater than the stress accumulated so far, the stress decreases only until it reaches $0$ .

Sangwon gets a stomachache on any day when the accumulated stress is at least $M$ . Find the number of days Sangwon suffers from stomachaches.

Input

The first line contains $N$ and $M$ , the number of days the stress changes were observed and the amount of stress that causes a stomachache.

The second line contains $A_1, A_2, \cdots ,A_N$ separated by spaces.

Output

Print the number of days on which Sangwon gets a stomachache.

Constraints

$1\leq N\leq 10^5$
$1\leq M\leq 10^9$
$-10^4\leq A_i\leq 10^4 (1\le i\le N)$
All input numbers are integers.

Examples2

Example 1
Input
```
10 10
2 -1 4 7 4 -8 3 6 4 -7
```
Expected output
```
6
```
Example 2
Input
```
5 1
1 -1 -1 -1 1
```
Expected output
```
2
```