E. Bus Video System

time limit per test

1 second

memory limit per test

256 megabytes

input

standard input

output

standard output

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

Copy

3 5
2 1 -3

output

Copy

3

input

Copy

2 4
-1 1

output

Copy

4

input

Copy

4 10
2 4 1 2

output

Copy

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 $\mathrm{00 or 11 passenger.}$

#include <iostream>
#include <bits/stdc++.h>
#define maxn 1005
using namespace std;
int a[maxn]={0};
int main()
{
    int n,w,i;
    scanf("%d%d",&n,&w);

    for(i=1;i<=n;i++)
    {
        scanf("%d",&a[i]);
    }
    int sum=0;
    int minum=1e9+5;
    int maxim=0;
    for(i=1;i<=n;i++)
    {   minum=min(minum,sum);
        maxim=max(maxim,sum);
        sum+=a[i];
    }
    minum=min(0,min(minum,sum));
    maxim=max(0,max(maxim,sum));
    if(abs(minum)>w||abs(maxim)>w)
    {
        printf("0
");
        return 0;
    }
    else
    {
       int l1=abs(minum);
       int r2=abs(w-maxim);
       int ans=r2-l1+1;
       if(ans<0) ans=0;
       cout<<ans<<endl;
    }
    return 0;
}