Some positive integers, not necessarily distinct, are written on a blackboard.
You are given these integers in a format that is specified at the end of this statement.
You are allowed to change the numbers on the blackboard in a sequence of steps.
In each step, you have to execute the following actions, in order:
(Above, gcd(x,y) denotes the greatest common divisor and lcm(x,y) the least common multiple of x and y.)
- Choose two numbers x and y on the blackboard.
- Erase x and y. (Erase exactly two numbers. If there are other copies of these numbers on the blackboard, leave them untouched.)
- Write two new integers onto the blackboard: gcd(x,y) and lcm(x,y).
You may perform arbitrarily many steps (possibly even zero).
Your goal is to maximize the sum of numbers written on the blackboard.
Let S be the largest possible sum.
Compute and return the value (S modulo 1,000,000,007).
You are given the ints start, d, and cnt, each with the same number of elements.
Use the following pseudocode to generate the numbers on the blackboard:
L = length(start)
for i = 0 .. L-1:
for j = 0 .. cnt[i]-1:
write the number (start[i] + j * d[i]) onto the blackboard
|Parameters:||int, int, int|
|Method signature:||int getMaximalSum(int start, int d, int cnt)|
|(be sure your method is public)|
|-||Note that you are maximizing the sum S. You are not maximizing the return value.|
|-||start, d and cnt will have the same number of elements.|
|-||start will contain between 1 and 500 elements, inclusive.|
|-||Each element of start and cnt will be between 1 and 10,000,000, inclusive.|
|-||Each element of d will be between 0 and 10,000,000, inclusive.|
|-||For each valid i, start[i] + d[i] * (cnt[i] - 1) will be at most 10,000,000.|
|-||The sum of all cnt[i] will be between 1 and 100,000, inclusive.|
There are three numbers on the blackboard: 1, 2 and 3. You can replace numbers 2 and 3 with numbers 1 and 6.
Then sum is 1 + 1 + 6 = 8 (which can be proved to be maximal). The answer is (8 modulo 1,000,000,007) = 8.
|There are five numbers 3 on the blackboard. It's impossible to change anything by performing described operations so the maximal sum is 15.|
|Numbers on the blackboard are 2, 4, 6, 8.|
|Numbers on the blackboard are 1, 3, 2, 5.|
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