Please subscribe to the official Codeforces channel in Telegram via the link: https://t.me/codeforces_official. ×

D3. The Wall (hard)
time limit per test
15 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

So many wall designs to choose from! Even modulo 106 + 3, it's an enormous number. Given that recently Heidi acquired an unlimited supply of bricks, her choices are endless! She really needs to do something to narrow them down.

Heidi is quick to come up with criteria for a useful wall:

  • In a useful wall, at least one segment is wider than W bricks. This should give the zombies something to hit their heads against. Or,
  • in a useful wall, at least one column is higher than H bricks. This provides a lookout from which zombies can be spotted at a distance.

This should rule out a fair amount of possibilities, right? Help Heidi compute the number of useless walls that do not confirm to either of these criteria. In other words, a wall is useless if every segment has width at most W and height at most H.

Parameter C, the total width of the wall, has the same meaning as in the easy version. However, note that the number of bricks is now unlimited.

Output the number of useless walls modulo 106 + 3.

Input

The first and the only line of the input contains three space-separated integers C, W and H (1 ≤ C ≤ 108, 1 ≤ W, H ≤ 100).

Output

Output the number of different walls, modulo 106 + 3, which are useless according to Heidi's criteria.

Examples
Input
1 1 1
Output
2
Input
1 2 2
Output
3
Input
1 2 3
Output
4
Input
3 2 2
Output
19
Input
5 4 9
Output
40951
Input
40 37 65
Output
933869
Note

If there is no brick in any of the columns, the structure is considered as a useless wall.