Codeforce 题目479E Riding in a Lift(DP)

E. Riding in a Lift

time limit per test

2 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

Imagine that you are in a building that has exactly n floors. You can move between the floors in a lift. Let's number the floors from bottom to top with integers from 1 to n. Now you're on the floor number a. You are very bored, so you want to take the lift. Floor number b has a secret lab, the entry is forbidden. However, you already are in the mood and decide to make k consecutive trips in the lift.

Let us suppose that at the moment you are on the floor number x (initially, you were on floor a). For another trip between floors you choose some floor with number y (y ≠ x) and the lift travels to this floor. As you cannot visit floor b with the secret lab, you decided that the distance from the current floor x to the chosen y must be strictly less than the distance from the current floor x to floor b with the secret lab. Formally, it means that the following inequation must fulfill: |x - y| < |x - b|. After the lift successfully transports you to floor y, you write down number y in your notepad.

Your task is to find the number of distinct number sequences that you could have written in the notebook as the result of k trips in the lift. As the sought number of trips can be rather large, find the remainder after dividing the number by 1000000007 (109 + 7).

Input

The first line of the input contains four space-separated integers n, a, b, k (2 ≤ n ≤ 5000, 1 ≤ k ≤ 5000, 1 ≤ a, b ≤ n, a ≠ b).

Output

Print a single integer — the remainder after dividing the sought number of sequences by 1000000007 (109 + 7).

Sample test(s)

input

5 2 4 1

output

2

input

5 2 4 2

output

2

input

5 3 4 1

output

0

Note

Two sequences p1, p2, ..., pk and q1, q2, ..., qk are distinct, if there is such integer j (1 ≤ j ≤ k), that pj ≠ qj.

Notes to the samples:

1. In the first sample after the first trip you are either on floor 1, or on floor 3, because |1 - 2| < |2 - 4| and |3 - 2| < |2 - 4|.
2. In the second sample there are two possible sequences: (1, 2); (1, 3). You cannot choose floor 3 for the first trip because in this case no floor can be the floor for the second trip.

1. In the third sample there are no sought sequences, because you cannot choose the floor for the first trip.

题目大意：给定n个楼层，初始在a层，b层不可停留，每次选一个楼层x，当|x-now| < |x-b| 且 x != now 时可达（now表示当前位置），此时记录下x到序列中，走k步，最后问有多少种可能的数的序列.

思路：

a<b:

dp[i][j]=sum[i][(j+b-1)/2]-dp[i-1][j]；上个位置只能在j和b的中点一下。找几个数据就得出结论了。

对于a>b:

将a，b关于对称轴对称下，那么问题就转化为a<b的问题

ac代码

#include<stdio.h>
#include<string.h>
#include<stdlib.h>
#include<iostream>
#include<algorithm>
#define mod 1000000007
using namespace std;
int dp[2][5050],sum[2][5050];
int n,a,b,k;
void getsum(int x)
{
    int i;
    for(i=1;i<=n;i++)
        sum[x%2][i]=(sum[x%2][i-1]+dp[x%2][i])%mod;
}
int main()
{
    //int n,a,b,k;
    while(scanf("%d%d%d%d",&n,&a,&b,&k)!=EOF)
    {
        if(a>b)
        {
            a=n-a+1;
            b=n-b+1;
        }
        memset(sum,0,sizeof(sum));
        memset(dp,0,sizeof(dp));
        dp[0][a]=1;
        getsum(0);
        int i,j;
        for(i=1;i<=k;i++)
        {
            for(j=1;j<b;j++)
            {
               dp[i%2][j]=(sum[(i-1)%2][(j+b-1)/2]-dp[(i-1)%2][j]+mod)%mod;
            }
            getsum(i);
        }
        int ans=0;
        for(i=1;i<=n;i++)
            ans=(ans+dp[k%2][i])%mod;
        printf("%d\n",ans);
    }
}