Katya and Segments Sets

It is a very important day for Katya. She has a test in a programming class. As always, she was given an interesting problem that she solved very fast. Can you solve that problem?

You are given n ordered segments sets. Each segment can be represented as a pair of two integers [l, r] where l≤ r. Each set can contain an arbitrary number of segments (even 0). It is possible that some segments are equal.

You are also given m queries, each of them can be represented as four numbers: a, b, x, y. For each segment, find out whether it is true that each set p (a≤ p≤ b) contains at least one segment [l, r] that lies entirely on the segment [x, y], that is x≤ l≤ r≤ y.

Find out the answer to each query.

Note that you need to solve this problem online. That is, you will get a new query only after you print the answer for the previous query.

Input

The first line contains three integers n, m, and k (1≤ n,m≤ 10^5, 1≤ k≤ 3⋅10^5) — the number of sets, queries, and segments respectively.

Each of the next k lines contains three integers l, r, and p (1≤ l≤ r≤ 10^9, 1≤ p≤ n) — the limits of the segment and the index of a set, to which this segment belongs.

Each of the next m lines contains four integers a, b, x, y (1≤ a≤ b≤ n, 1≤ x≤ y≤ 10^9) — the description of the query.

Output

For each query, print "yes" or "no" in a new line.

Interaction

After printing a query, do not forget to output end of line and flush the output. Otherwise, you will get Idleness limit exceeded. To do this, use:

• fflush(stdout) or cout.flush() in C++;
• System.out.flush() in Java;
• flush(output) in Pascal;
• stdout.flush() in Python;
• see documentation for other languages.

Example

Input

5 5 9 3 6 3 1 3 1 2 4 2 1 2 3 4 6 5 2 5 3 7 9 4 2 3 1 4 10 4 1 2 2 3 1 2 2 4 1 3 1 5 2 3 3 6 2 4 2 9

Output

no yes yes no yes

Note

For the first query, the answer is negative since the second set does not contain a segment that lies on the segment [2, 3].

In the second query, the first set contains [2, 3], and the second set contains [2, 4].

In the third query, the first set contains [2, 3], the second set contains [2, 4], and the third set contains [2, 5].

In the fourth query, the second set does not contain a segment that lies on the segment [3, 6].

In the fifth query, the second set contains [2, 4], the third set contains [2, 5], and the fourth contains [7, 9].

inputFormat

Input

The first line contains three integers n, m, and k (1≤ n,m≤ 10^5, 1≤ k≤ 3⋅10^5) — the number of sets, queries, and segments respectively.

Each of the next k lines contains three integers l, r, and p (1≤ l≤ r≤ 10^9, 1≤ p≤ n) — the limits of the segment and the index of a set, to which this segment belongs.

Each of the next m lines contains four integers a, b, x, y (1≤ a≤ b≤ n, 1≤ x≤ y≤ 10^9) — the description of the query.

outputFormat

Output

For each query, print "yes" or "no" in a new line.

Interaction

After printing a query, do not forget to output end of line and flush the output. Otherwise, you will get Idleness limit exceeded. To do this, use:

• fflush(stdout) or cout.flush() in C++;
• System.out.flush() in Java;
• flush(output) in Pascal;
• stdout.flush() in Python;
• see documentation for other languages.

Example

Input

5 5 9 3 6 3 1 3 1 2 4 2 1 2 3 4 6 5 2 5 3 7 9 4 2 3 1 4 10 4 1 2 2 3 1 2 2 4 1 3 1 5 2 3 3 6 2 4 2 9

Output

no yes yes no yes

Note

For the first query, the answer is negative since the second set does not contain a segment that lies on the segment [2, 3].

In the second query, the first set contains [2, 3], and the second set contains [2, 4].

In the third query, the first set contains [2, 3], the second set contains [2, 4], and the third set contains [2, 5].

In the fourth query, the second set does not contain a segment that lies on the segment [3, 6].

In the fifth query, the second set contains [2, 4], the third set contains [2, 5], and the fourth contains [7, 9].

样例

5 5 9
3 6 3
1 3 1
2 4 2
1 2 3
4 6 5
2 5 3
7 9 4
2 3 1
4 10 4
1 2 2 3
1 2 2 4
1 3 1 5
2 3 3 6
2 4 2 9

no
yes
yes
no
yes

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