Given two numbers N and T where, and . The task is to find the value of .
Since sum can be large, output it modulo 109+7.
Input : 3 2 Output : 38 2*3 + 3*4 + 4*5 = 38 Input : 4 2 Output : 68
In the Given Sample Case n = 3 and t = 2.
sum = 2*3+3*4+4*5.
So each term is of the form
If we multiply and divide by t! it becomes
Which is nothing but
But we know
So final expression comes out to be
But since n is so large we can not calculate it directly, we have to Simplify the above expression.
On Simplifying we get .
Below is the implementation of above approach
Time Complexity: O(T)
- Find the Number of Maximum Product Quadruples
- Find the number in a range having maximum product of the digits
- Find Nth number of the series 1, 6, 15, 28, 45, .....
- Program to find the Nth number of the series 2, 10, 24, 44, 70.....
- Count number of triplets with product equal to given number with duplicates allowed | Set-2
- Count number of triplets with product equal to given number with duplicates allowed
- Sum and Product of digits in a number that divide the number
- Find two numbers with sum and product both same as N
- Find the Product of first N Prime Numbers
- Find if n can be written as product of k numbers
- Find N integers with given difference between product and sum
- Find four factors of N with maximum product and sum equal to N
- Find four factors of N with maximum product and sum equal to N | Set 3
- Find four factors of N with maximum product and sum equal to N | Set-2
- Find two distinct prime numbers with given product
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