CF978E.Bus Video System

普及/提高-

通过率：0%

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题目描述

The first line contains two integers $n$ and $w$ $(1 \le n \le 1\,000, 1 \le w \le 10^{9})$ — the number of bus stops and the capacity of the bus.

The second line contains a sequence $a_1, a_2, \dots, a_n$ $(-10^{6} \le a_i \le 10^{6})$ , where $a_i$ equals to the number, which has been recorded by the video system after the $i$ -th bus stop.

输入格式

Print the number of possible ways how many people could be in the bus before the first bus stop, if the bus has a capacity equals to $w$ . If the situation is contradictory (i.e. for any initial number of passengers there will be a contradiction), print 0.

输出格式

In the first example initially in the bus could be $0$ , $1$ or $2$ passengers.

In the second example initially in the bus could be $1$ , $2$ , $3$ or $4$ passengers.

In the third example initially in the bus could be $0$ or $1$ passenger.

输入输出样例

输入#1
```
3 5
2 1 -3
```
输出#1
```
3
```
输入#2
```
2 4
-1 1
```
输出#2
```
4
```
输入#3
```
4 10
2 4 1 2
```
输出#3
```
2
```

说明/提示

In the first example initially in the bus could be $0$ , $1$ or $2$ passengers.

In the second example initially in the bus could be $1$ , $2$ , $3$ or $4$ passengers.

In the third example initially in the bus could be $0$ or $1$ passenger.

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