Recently IMO 2015 has ended. Problem 6 was the hardest one and solved by only 11 contestants, but for competitive programmers this task wasn't that hard. If you are interested in it, I think it's worth trying even if you haven't solved any IMO problems.
The problem statement is here.
I wrote some hints in white characters.
Hint 1: How is it related to competitive programming?
Hint 2: Doesn't it look like bitmask DP?
Hint 3: Run the following program.
mask = 0;
mask» = 1;
mask| = (1«(ai - 1)); // here the newly set bit must be 0 before this operation
Hint 4: The number of '1' bits in mask is non-decreasing while the program is running.
So, the number of '1' bits will be constant at some moment: call it b.
Then, the sum of (aj - b) is the difference of sum of positions of set bits in mask when i = m and i = n.