CareerCup

There are N stations in a certain region, numbered 1 through N. It takes di,j minutes to travel from Station i to Station j (1 ¥leq i, j ¥leq N)$. Note that di,j=dj,i may not hold.
You are now at Station 1. From here, you have to visit all the stations exactly once. We assume that you have already visited Station 1. However, due to your schedule, there are M restrictions that must be satisfied. The format of each restriction is as follows:
• Station si must be visited before Station ti. (1≤i≤M)
Find the minimum time required to visit all the stations. Note that the last station to visit can be any of the stations.
Constraints
• 1≤N≤14
• 0≤di,j≤108 (1≤i,j≤N)
• di,i=0 (1≤i≤N)
• 0≤M≤N(N−1)⁄2
• 1≤si,ti≤N (1≤i≤M)
• si≠ti (1≤i≤M)
• There exists a path visiting all the stations under the given restrictions.
Input
Input is given from Standard Input in the following format: N d1,1 … d1,N : dN,1 … dN,N M s1 t1 : sM tM
Output
Print the minimum time required to visit all the stations.
Sample Input 1
4
0 2 3 4
1 0 3 4
1 2 0 4
1 2 3 0
3
1 2
2 3
3 4
Sample Output 1
9
Due to the restrictions, we can only travel as follows: Station 1 → Station 2 → Station 3 → Station 4. Thus, the answer is 2+3+4=9 and we should print 9.
Sample Input 2
3
0 1 20
1 0 20
10 20 0
0
Sample Output 2
21

You are given an array of length N consisting of integers, a={a1,…,aN}, and an integer L.
Consider the following subproblem:
• You are given an integer S.
• Find the largest value in the interval [S,S+L−1] in the sequence a, that is, find max(aS,…,aS+L−1).
Solve this subproblem for every S=1,…,N−L+1.
Constraints
• 1≤N≤105
• 1≤L≤N
• −109≤ai≤109
Input
Input is given from Standard Input in the following format: N L a1 … aN
Output
Print the answers in N−L+1 lines. The i-th line should contain the answer to the subproblem where S=i.
Sample Input 1
5 3
3 4 2 1 5
Sample Output 1
4
4
5
• The subproblem where S=1 asks the largest value among a={a1,a2,a3}={3,4,2}, so the first line in the output should contain 4.
• The subproblem where S=2 asks the largest value among a={a2,a3,a4}={4,2,1}, so the second line in the output should contain 4.
• The subproblem where S=3 asks the largest value among a={a3,a4,a5}={2,1,5}, so the third line in the output should contain 5.
Sample Input 2
4 1
-1000000000 1000000000 -1000000000 1000000000
Sample Output 2
-1000000000
1000000000
-1000000000
1000000000

There are N rooms in a row. The i-th room (1≤i≤N) from the left is called Room i. You are given M closed intervals [ai,bi] (1≤i≤M). At time 0, all rooms j such that ai≤j≤bi for some i (1≤i≤M) are occupied, and the other rooms are vacant.
You are given Q queries. The i-th query (1≤i≤Q) represents an event happening at time i, as follows:
• In the i-th query (1≤i≤Q), a closed interval [ci,di] (1≤i≤Q) is given.
• This query asks: "Are all rooms j such that ci≤j≤ci" vacant?
• If all those rooms are vacant, the query should be responded by OK, then all rooms j such that ci≤j≤ci get occupied.
• Otherwise, the query should be responded by OK, then nothing happens.
Process these queries.
Constraints
• 1≤N≤109
• 0≤M≤1000
• 1≤ai≤bi≤N (1≤i≤M)
• There are no rooms k such that ai≤k≤bi and aj≤k≤bj at the same time (1≤i<j≤M).
• 1≤Q≤1000
• 1≤ci≤di≤N
Input
Input is given from Standard Input in the following format: N M a1 b1 : aM bM Q c1 d1 : cQ dQ
Output
Print the responses in Q lines. The i-th line should contain the response to the i-th query.
Sample Input 1
5 2
1 1
4 4
3
3 3
2 3
5 5
Sample Output 1
OK
NG
OK
At time 0, Room 1 and 4 are occupied.
• At time 1, a query asks: "is Room 3 occupied?" Since Room 3 is vacant, we should print OK, then Room 3 gets occupied.
• At time 2, a query asks: "are Room 2 and 3 occupied?" Since Room 3 is occupied, we should print NG.
• At time 3, a query asks: "is Room 5 occupied?" Since Room 5 is vacant, we should print OK, then Room 5 gets occupied.
Sample Input 2
1000000000 1
2 999999999
4
1 1000000000
500000000 500000000
1 1
1000000000 1000000000
Sample Output 2
NG
NG
OK
OK

You are given N records. The content of the i-th record is represented by a string Si. These records are managed in pages, as follows:
• The first page: contains the first, ..., K-th records.
• The second page: contains the (K+1)-th, ..., 2K-th records.
• The third page: contains the (2K+1)-th, ..., 3K-th records.
• :
• The ceil(N⁄K)-th page: contains the ((ceil(N⁄K)−1)K+1)-th, ..., N-th records.
Here, ceil(X) represents the smallest integer not less than X. Print the contents of the records contained in the M-th page, in the order given.
Constraints
• 1≤N≤100
• 1≤K≤N
• 1≤M≤ceil(N⁄K)
• 1≤|Si|≤100 (1≤i≤N), where |S| is the length of S.
• Si is a string consisting of lowercase English letters.
Input
Input is given from Standard Input in the following format:
N K M S1 S2 : SN
Output
Print the contents of the records contained in the M-th page, in the order given. Use L lines, where L is the number of records that should be printed. The i-th line (1≤i≤L) should contain the content of the i-th record contained in the M-th page.
Sample Input 1
5 2 2
aaa
bbb
ccc
ddd
eee
Sample Output 1
ccc
ddd
• The first page contains the first and second records, which are aaa and bbb.
• The second page contains the third and fourth records, which are ccc and ddd.
• The third page contains the fifth record, which is eee.
Since the second page is requested, we should print ccc in the first line and ddd in the second line.
Sample Input 2
7 4 2
this
is
not
displayed
this
is
displayed
Sample Output 2
this
is
displayed

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