E. Team Work
combinatorics; dp; math
You have a team of N people. For a particular task, you can pick any non-empty subset of people. The cost of having x people for the task is xk. Output the sum of costs over all non-empty subsets of people.
Only line of input contains two integers N (1 ≤ N ≤ 109) representing total number of people and k (1 ≤ k ≤ 5000).
Output the sum of costs for all non empty subsets modulo 109 + 7.
In the first example, there is only one non-empty subset {1} with cost 11 = 1.In the second example, there are seven non-empty subsets.- {1} with cost 12 = 1- {2} with cost 12 = 1- {1, 2} with cost 22 = 4- {3} with cost 12 = 1- {1, 3} with cost 22 = 4- {2, 3} with cost 22 = 4- {1, 2, 3} with cost 32 = 9The total cost is 1 + 1 + 4 + 1 + 4 + 4 + 9 = 24.