Problem2194--A Museum Robbery

2194: A Museum Robbery

Time Limit: 2 Sec  Memory Limit: 256 MB
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Description

time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

There's a famous museum in the city where Kleofas lives. In the museum, n exhibits (numbered 1 through n) had been displayed for a long time; the i-th of those exhibits has value vi and mass wi.

Then, the museum was bought by a large financial group and started to vary the exhibits. At about the same time, Kleofas... gained interest in the museum, so to say.

You should process q events of three types:

  • type 1 − the museum displays an exhibit with value v and mass w; the exhibit displayed in the i-th event of this type is numbered n+i (see sample explanation for more details)
  • type 2 − the museum removes the exhibit with number x and stores it safely in its vault
  • type 3 − Kleofas visits the museum and wonders (for no important reason at all, of course): if there was a robbery and exhibits with total mass at most m were stolen, what would their maximum possible total value be?

For each event of type 3, let s(m) be the maximum possible total value of stolen exhibits with total mass ≤m.

Formally, let D be the set of numbers of all exhibits that are currently displayed (so initially D = {1, ..., n}). Let P(D) be the set of all subsets of D and let

Then, s(m) is defined as

Compute s(m) for each . Note that the output follows a special format.

Input

The first line of the input contains two space-separated integers n and k (1≤n≤5000, 1≤k≤1000) − the initial number of exhibits in the museum and the maximum interesting mass of stolen exhibits.

Then, n lines follow. The i-th of them contains two space-separated positive integers vi and wi (1≤vi≤1000000, 1≤wi≤1000)− the value and mass of the i-th exhibit.

The next line contains a single integer q (1≤q≤30000)− the number of events.

Each of the next q lines contains the description of one event in the following format:

  • 1 v w − an event of type 1, a new exhibit with value v and mass w has been added (1≤v≤1000000, 1≤w≤1000)
  • 2 x − an event of type 2, the exhibit with number x has been removed; it's guaranteed that the removed exhibit had been displayed at that time
  • 3 − an event of type 3, Kleofas visits the museum and asks his question

There will be at most 10000 events of type 1 and at least one event of type 3.

Output

As the number of values s(m) can get large, output the answers to events of type 3 in a special format.

For each event of type 3, consider the values s(m) computed for the question that Kleofas asked in this event; print one line containing a single number

where p=107+19 and q=109+7.

Print the answers to events of type 3 in the order in which they appear in the input.

Examples
Input
3 10
30 4
60 6
5 1
9
3
1 42 5
1 20 3
3
2 2
2 4
3
1 40 6
3
Output
556674384
168191145
947033915
181541912
Input
3 1000
100 42
100 47
400 15
4
2 2
2 1
2 3
3
Output
0
Note

In the first sample, the numbers of displayed exhibits and values s(1),...,s(10) for individual events of type 3 are, in order:

The values of individual exhibits are v1=30,v2=60,v3=5,v4=42,v5=20,v6=40 and their masses are w1=4,w2=6,w3=1,w4=5,w5=3,w6=6.

In the second sample, the only question is asked after removing all exhibits, so s(m)=0 for any m.

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