CodeForces - 471D MUH and Cube Walls (kmp)

Polar bears Menshykov and Uslada from the zoo of St. Petersburg and elephant Horace from the zoo of Kiev got hold of lots of wooden cubes somewhere. They started making cube towers by placing the cubes one on top of the other. They defined multiple towers standing in a line as a wall. A wall can consist of towers of different heights.

Horace was the first to finish making his wall. He called his wall an elephant. The wall consists of w towers. The bears also finished making their wall but they didn't give it a name. Their wall consists of n towers. Horace looked at the bears' tower and wondered: in how many parts of the wall can he "see an elephant"? He can "see an elephant" on a segment of w contiguous towers if the heights of the towers on the segment match as a sequence the heights of the towers in Horace's wall. In order to see as many elephants as possible, Horace can raise and lower his wall. He even can lower the wall below the ground level (see the pictures to the samples for clarification).

Your task is to count the number of segments where Horace can "see an elephant".

Input

The first line contains two integers n and w (1 ≤ n, w ≤ 2·10⁵) — the number of towers in the bears' and the elephant's walls correspondingly. The second line contains n integers a_i (1 ≤ a_i ≤ 10⁹) — the heights of the towers in the bears' wall. The third line contains w integers b_i (1 ≤ b_i ≤ 10⁹) — the heights of the towers in the elephant's wall.

Output

Print the number of segments in the bears' wall where Horace can "see an elephant".

Examples

Input

13 5
2 4 5 5 4 3 2 2 2 3 3 2 1
3 4 4 3 2

Output

2

Note

The picture to the left shows Horace's wall from the sample, the picture to the right shows the bears' wall. The segments where Horace can "see an elephant" are in gray.

题意:输入 a数组和b数组 ，要你求 a数组中有几个b数组 （a中数组可以与b数组的值有个相同且固定的差值）

解 : 你先把 a数组更改一下 比如 a[i]=a[i+1]-a[i]            b[i]=b[i+1]-b[i];

显然两个数之间的差值 a 和 b应该是相同的，然后kmp

#include<stdio.h>
#include<string.h>
#include<math.h>
#include<queue>
#include<algorithm>
#define inf 0x3f3f3f3f
#define ll long long
#define maxx 5000005
using namespace std;
int n,m;
int s[1000000];
int p[1000000];
int nex[1000000];
void kk()
{
    int i,j;
    j=nex[0]=-1;
    i=0;
    while(i<m-1)
    {
        while(-1!=j&&p[i]!=p[j]) j=nex[j];
        nex[++i]=++j;
    }
}
int kmp()
{
    int i,j;
    int ans=0;
    kk();
    i=j=0;
    while(i<n-1)
    {
        while(-1!=j&&s[i]!=p[j]) j=nex[j];
        i++;j++;
        if(j>=m-1)
        {
            ans++;
            j=nex[j];
        }
    }
    return ans;
}
int main()
{
    scanf("%d%d",&n,&m);
    for(int i=0;i<n;i++)
        scanf("%d",&s[i]);
    for(int i=0;i<m;i++)
     scanf("%d",&p[i]);
     for(int i=0;i<n-1;i++)
        s[i]=s[i+1]-s[i];
     for(int i=0;i<m-1;i++)
        p[i]=p[i+1]-p[i];
     if(m==1)//如果m=1，特判
    printf("%d\n",kmp()+1);
    else 
    printf("%d\n",kmp());

}