CF978E.Bus Video System

The busses in Berland are equipped with a video surveillance system. The system records information about changes in the number of passengers in a bus after stops.

If $x$ is the number of passengers in a bus just before the current bus stop and $y$ is the number of passengers in the bus just after current bus stop, the system records the number $y-x$. So the system records show how number of passengers changed.

The test run was made for single bus and $n$ bus stops. Thus, the system recorded the sequence of integers $a_1, a_2, \dots, a_n$ (exactly one number for each bus stop), where $a_i$ is the record for the bus stop $i$. The bus stops are numbered from $1$ to $n$ in chronological order.

Determine 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 $w$ (that is, at any time in the bus there should be from $0$ to $w$ passengers inclusive).

贝尔兰的公交车配备了视频监控系统。该系统记录每次公交站点上下车后车上乘客数量的变化情况。

若 $x$ 表示公交车在当前站点停靠前的乘客人数，$y$ 表示公交车在当前站点停靠后的乘客人数，则系统记录数值 $y-x$。因此，系统记录反映的是乘客人数的变化量。

本次测试运行针对一辆公交车和 $n$ 个公交站点进行。因此，系统记录了一组整数序列 $a_1, a_2, \dots, a_n$（每个站点恰好对应一个数），其中 $a_i$ 是第 $i$ 个站点的记录值。公交站点按时间顺序编号为 $1$ 至 $n$。

请确定：在公交车容量为 $w$（即任意时刻车上乘客人数必须在 $0$ 到 $w$ 之间，含端点）的前提下，公交车在第一个站点停靠前可能的乘客人数有多少种取值？

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.

第一行包含两个整数 $n$ 和 $w$ $(1 \le n \le 1\,000, 1 \le w \le 10^{9})$ —— 分别表示公交站点的数量和公交车的容量。

第二行包含一个序列 $a_1, a_2, \dots, a_n$ $(-10^{6} \le a_i \le 10^{6})$，其中 $a_i$ 表示视频系统在第 $i$ 个公交站点之后记录的数值。

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.

打印在第一个公交站之前车上可能的乘客人数的方案数，已知公交车的容量为 $w$。如果该情况自相矛盾（即：无论初始乘客数取何值，都会出现矛盾），则输出 0。

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.

在第一个例子中，公交车上最初可能有 $0$、$1$ 或 $2$ 名乘客。

在第二个例子中，公交车上最初可能有 $1$、$2$、$3$ 或 $4$ 名乘客。

在第三个例子中，公交车上最初可能有 $0$ 或 $1$ 名乘客。