PKU 1989. The Cow Lineup

The Cow Lineup

Time Limit: 1000MS	Memory Limit: 30000K
Total Submissions: 3397	Accepted: 2028

Description

Farmer John's N cows (1 <= N <= 100,000) are lined up in a row.Each cow is labeled with a number in the range 1...K (1 <= K <=10,000) identifying her breed. For example, a line of 14 cows might have these breeds: 

    1 5 3 2 5 1 3 4 4 2 5 1 2 3

Farmer John's acute mathematical mind notices all sorts of properties of number sequences like that above. For instance, he notices that the sequence 3 4 1 3 is a subsequence (not necessarily contiguous) of the sequence of breed IDs above. FJ is curious what is the length of the shortest possible sequence he can construct out of numbers in the range 1..K that is NOT a subsequence of the breed IDs of his cows. Help him solve this problem. 

Input

* Line 1: Two integers, N and K 

* Lines 2..N+1: Each line contains a single integer that is the breed ID of a cow. Line 2 describes cow 1; line 3 describes cow 2; and so on. 

Output

* Line 1: The length of the shortest sequence that is not a subsequence of the input 

Sample Input

14 5
1
5
3
2
5
1
3
4
4
2
5
1
2
3

Sample Output

3

Hint

All the single digit 'sequences' appear. Each of the 25 two digit sequences also appears. Of the three digit sequences, the sequence 2, 2, 4 does not appear. 

Source

USACO 2004 U S Open