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Allied Nations' Tour

Problem Description

As we all know the five great nations have come together in order to fight Madra Uchiha. As these five nations have combined travelling in them has become quite difficult.

The allied nations in total have A cities numbered from 1 to A. Currently you are at city B. Your task is take a tour of among given A cities for C days. From a city i you can go to any city in the range i-E to i+E and you can not go out of range. It is not necessary to visit all the cities, you just have to take a tour for C days. Two tours will be different from each other if there is some day in which both visitied different cities.

However the intel core has provided M information given in form of 2D array D of size M. According to this at day D[i][0] Akatsuki will attack on city D[i][1]. You are to avoid any collision with the Akatsuki. You can not be present in some city on a certain day if Akatsuki will arrive there.

Find the total number of tours you will be able to take. Since the answer can be big output it %1000000007



Problem Constraints
1 <= A, C <= 1000

1 <= M <= AC

1 <= B <= A

1 <= D[i][0] <= C

1 <= D[i][1] <= A

1 <= E <= A


Input Format
First argument contains integer A.
Second argument contains starting city B.
Third argument contains number of days C.
Fourth argument contains intel in form D.


Output Format
Return a single integer as the answer to the question.


Example Input
Input 1:

A = 2
B = 2
C = 5
D = [ [5, 1], 
      [3, 1],
      [4, 2],
      [2, 1],
      [1, 2]
    ]
E = 1


Input 2:

A = 4
B = 1
C = 4
D = []
E = 4



Example Output
Output 1:

1


Output 2:

256



Example Explanation*
Explanation 1:

For day 1, we can only go to city 1.
For day 2, we can only go to city 2 from 1.
For day 3, we can only go to city 2 from 2.
For day 4, we can only go to city 2 from 2.
For final day, we can only go to city  2 from 2.

Hence there is only one tour available : 1, 2, 2, 2, 2


Explanation 2:

We can choose any city on any day. Hence ans = 444*4 = 256



NOTE: You only need to implement the given function. Do not read input, instead use the arguments to the function. Do not print the output, instead return values as specified. Still have a question? Checkout Sample Codes for more details.
Start solving Allied Nations' Tour on Interview Code Editor
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