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 $\mathrm{xx is\; the\; number\; of\; passengers\; in\; a\; bus\; just\; before\; the\; current\; bus\; stop\; and yy is\; the\; number\; of\; passengers\; in\; the\; bus\; just\; after\; current\; bus\; stop,\; the\; system\; records\; the\; number y-xy-x.\; So\; the\; system\; records\; show\; how\; number\; of\; passengers\; changed.}$

The test run was made for single bus and $\mathrm{nn bus\; stops.\; Thus,\; the\; system\; recorded\; the\; sequence\; of\; integers a1,a2,\dots ,ana1,a2,\dots ,an (exactly\; one\; number\; for\; each\; bus\; stop),\; where aiai is\; the\; record\; for\; the\; bus\; stop ii.\; The\; bus\; stops\; are\; numbered\; from 11 to nn in\; chronological\; order.}$

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 $\mathrm{ww (that\; is,\; at\; any\; time\; in\; the\; bus\; there\; should\; be\; from 00 to ww passengers\; inclusive).}$

Input

The first line contains two integers $\mathrm{nn and ww (1\le n\le 1000,1\le w\le 109)(1\le n\le 1000,1\le w\le 109) —\; the\; number\; of\; bus\; stops\; and\; the\; capacity\; of\; the\; bus.}$

The second line contains a sequence ${\mathrm{a1,a2,\dots ,ana1,a2,\dots ,an (-106\le ai\le 106)(-106\le ai\le 106),\; where aiai equals\; to\; the\; number,\; which\; has\; been\; recorded\; by\; the\; video\; system\; after\; the ii-th\; bus\; stop.}}^{}$

Output

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 $\mathrm{ww.\; If\; the\; situation\; is\; contradictory\; (i.e.\; for\; any\; initial\; number\; of\; passengers\; there\; will\; be\; a\; contradiction),\; print 0.}$

Examples

input

3 5
2 1 -3

output

3

input

2 4
-1 1

output

4

input

4 10
2 4 1 2

output

2

Note

In the first example initially in the bus could be $\mathrm{00, 11 or 22 passengers.}$

In the second example initially in the bus could be $\mathrm{11, 22, 33 or 44 passengers.}$

In the third example initially in the bus could be $\mathrm{00 or 11 passenger.}$

题解：

只需要从后向前找出人最多的时刻，和最少的时刻。

#include <bits/stdc++.h>
using namespace std;
const int MAXN=200010;
const int INF=0x3f3f3f3f;
int sum[MAXN];

int main()
{
    int n,w,a;
    scanf("%d%d",&n,&w);
    int MAX=0,MIN=INF;
    for (int i = 1; i <=n ; ++i) {
        scanf("%d",&a);
        sum[i]=sum[i-1]+a;
        MAX=max(MAX,sum[i]);
        MIN=min(MIN,sum[i]);
    }
    MAX=w-MAX;
    MIN=MIN>0?0:-MIN;
    if(MAX-MIN+1<0) printf("0
");
    else printf("%d
",MAX-MIN+1);

    return 0;
}