Problem Statement  
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:
 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).
(Above, gcd(x,y) denotes the greatest common divisor and lcm(x,y) the least common multiple of x and 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 int[]s 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 .. L1:
for j = 0 .. cnt[i]1:
write the number (start[i] + j * d[i]) onto the blackboard
  Definition   Class:  GCDLCM2  Method:  getMaximalSum  Parameters:  int[], int[], int[]  Returns:  int  Method signature:  int getMaximalSum(int[] start, int[] d, int[] cnt)  (be sure your method is public) 
    Notes    Note that you are maximizing the sum S. You are not maximizing the return value.   Constraints    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.   Examples  0)     Returns: 8 
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.


 1)     Returns: 15  There are five numbers 3 on the blackboard. It's impossible to change anything by performing described operations so the maximal sum is 15. 

 2)     Returns: 32  Numbers on the blackboard are 2, 4, 6, 8. 

 3)     Returns: 33  Numbers on the blackboard are 1, 3, 2, 5. 

 4)    {5 ,6}  {23, 45}  {50000, 50000} 
 Returns: 804225394  

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