INCSEQ - Increasing Subsequences

Given a sequence of N (1 ≤ N ≤ 10,000) integers S1, ..., SN (0 ≤ Si < 100,000), compute the number of increasing subsequences of S with length K (1 ≤ K ≤ 50 and K ≤ N); that is, the number of K-tuples i1, ..., iK such that 1 ≤ i1 < ... < iK ≤ N and Si1 < ... < SiK.

Input

The first line contains the two integers N and K. The following N lines contain the integers of the sequence in order.

Output

Print a single integer representing the number of increasing subsequences of S of length K, modulo 5,000,000.

Example

Input:
4 3
1
2
2
10

Output:
2

The two 3-tuples are (1, 2, 4) and (1, 3, 4), both corresponding to the subsequence 1, 2, 10.


Added by:Neal Wu
Date:2008-06-20
Time limit:1s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ERL JS-RHINO
Resource:

hide comments
2023-08-28 07:46:17
SEGMENT Tree is like Sigma whereas BIT is like Beta, visualisation is very simple for Segment Tree. Use 50 STs.

Last edit: 2023-08-28 07:46:59
2020-07-16 11:08:22 Rishabh Agrawal
Can also be done in O(n*k*logn) using mergesort like technique
2020-03-22 19:05:58
Finally solved it using DP + 2D-BIT
2020-02-27 11:38:55
keep consider that someties BIT can't return value of index 0
finally solved DP+BIT
2019-10-13 08:35:47
if u r getting WA on test 10 make sure u hv taken care of 0's int the input
2019-06-14 07:51:18
Note that array S can have zero.

Last edit: 2019-06-14 07:52:48
2019-03-30 21:56:34
go in 1 AC!
2019-03-27 21:52:48
solved it using bitset optimization, no wonder I won gold at IOI 2019
2019-03-27 16:13:50
i wholeheadedly reccomend this task!
2019-01-21 16:41:11
DP+BIT = AC
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