This problem is a programming version of Problem 212 from projecteuler.net
An axis-aligned cuboid, specified by parameters { }, consists of all points such that , , . The volume of the cuboid is the product, . The combined volume of a collection of cuboids is the volume of their union and will be less than the sum of the individual volumes if any cuboids overlap.
Let be a collection of axis-aligned cuboids such that has parameters
modulo
modulo
modulo
modulo
modulo
modulo
where come from the "Lagged Fibonacci Generator":
For modulo
For modulo
For example, if and , then has parameters {}, has parameters {}, and so on.
With such , and , the combined volume of the first cuboids, , is .
What is the combined volume of cuboids, ?
Input Format
The only line of each test file contains exactly seven space-separated integers: , and .
Constraints
Output Format
Print exactly one number: the combined volume of cuboids.
Sample Input 0
53 54 48 257 51 81 2
Sample Output 0
88970
Explanation 0
With the given and the cuboid has parameters { } and the cuboid has parameters { }.
It is clear that the cuboid is within the boundaries of the cuboid therefore the combined volume of the two cuboids equals to the volume of the second cuboid which is
.
Sample Input 1
4649 7681 6382 113 75 93 2
Sample Output 1
538384
Explanation 1
With the given and the cuboid has parameters { } and the cuboid has parameters { }.
With such small cuboid sizes, it is clear that the cuboids have no overlap therefore the combined volume of the two cuboids equals to the sum of their volumes which is
.
Sample Input 2
10000 10000 10000 399 399 399 100
Sample Output 2
723581599
Explanation 2
As noted in the problem statement.