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In this even odd problem Given a range [low, high] (both inclusive), select K numbers from the range (a number can be chosen multiple times) such that sum of those K numbers is even.

Calculate the number of all such permutations.

As this number can be large, print it modulo (1e9 +7).

Constraints

0 <= low <= high <= 10^9
K <= 10^6.

Input

First line contains two space separated integers denoting low and high respectively
Second line contains a single integer K.

Output

Print a single integer denoting the number of all such permutations Input

First line contains two space separated integers denoting low and high respectively
Second line contains a single integer K.

Output

Print a single integer denoting the number of all such permutations

Input : 4 5

3

Output :

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432 / 434

Roco is an island near Africa which is very prone to forest fire. Forest fire is such that it destroys the complete forest. Not a single tree is left.This island has been cursed by God , and the curse is that whenever a tree catches fire, it passes the fire to all its adjacent tree in all 8 directions,North, South, East, West, North-East, North-West, South-East, and South-West.And it is given that the fire is spreading every minute in the given manner, i.e every tree is passing fire to its adjacent tree.Suppose that the forest layout is as follows where T denotes tree and W denotes water.

Your task is that given the location of the first tree that catches fire, determine how long would it take for the entire forest to be on fire. You may assume that the lay out of the forest is such that the whole forest will catch fire for sure and that there will be at least one tree in the forest

Input Format:

First line contains two integers, M, N, space separated, giving the size of the forest in terms of the number of rows and columns respectively.
The next line contains two integers X,Y, space separated, giving the coordinates of the first tree that catches the fire.
The next M lines, where ith line containing N characters each of which is either T or W, giving the position of the Tree and Water in the ith row of the forest.

Output Format:

Single integer indicating the number of minutes taken for the entire forest to catch fire

Input : 3 3
W T T
T W W
W T T

Output :

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433 / 434

Compute the nearest larger number by interchanging its digits updated.Given 2 numbers a and b find the smallest number greater than b by interchanging the digits of a and if not possible print -1.

Input Format
2 numbers a and b, separated by space.

Output Format
A single number greater than b.

If not possible, print -1

Constraints

1 <= a,b <= 10000000

Input : 459 500

Output :

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434 / 434

In a Conference ,attendees are invited for a dinner after the conference.The Co-ordinator,Sagar arranged around round tables for dinner and want to have an impactful seating experience for the attendees.Before finalizing the seating arrangement,he wants to analyze all the possible arrangements.These are R round tables and N attendees.In case where N is an exact multiple of R,the number of attendees must be exactly N//R,,If N is not an exact multiple of R, then the distribution of attendees must be as equal as possible.Please refer to the example section before for better understanding.
For example, R = 2 and N = 3
All possible seating arrangements are
(1,2) & (3)
(1,3) & (2)
(2,3) & (1)
Attendees are numbered from 1 to N.

Input Format:

The first line contains T denoting the number of test cases.
Each test case contains two space separated integers R and N, Where R denotes the number of round tables and N denotes the number of attendees.

Output Format:

Single Integer S denoting the number of possible unique arrangements.

Constraints:

0 <= R <= 10(Integer)
0 < N <= 20 (Integer)

Input : 1
2 5

Output :

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