Description

Farmer John has a binary string of length $N$ $(1 \leq N \leq 10^9)$, initially all zeros.

He will first perform $M$ ($1 \leq M \leq 2 \cdot 10^5$) updates on the string, in order. Each update flips every character from $l$ to $r$. Specifically, flipping a character changes it from $0$ to $1$, or vice versa.

Then, he asks you $Q$ ($1 \leq Q \leq 2 \cdot 10^5$) queries. For each query, he asks you to output the lexicographically greatest subsequence of length $k$ comprised of characters from the substring from $l$ to $r$. If your answer is a binary string $s_1s_2 \dots s_k$, then output $\sum_{i=0}^{k-1} 2^i \cdot s_{k-i}$ (that is, its value when interpreted as a binary number) modulo $10^9+7$.

A subsequence is a string that can be derived from another string by deleting some or no characters without changing the order of the remaining characters.

Recall that string $A$ is lexicographically greater than string $B$ of equal length if and only if at the first position $i$, if it exists, where $A_i \neq B_i$, we have $A_i > B_i$.

Input Format

The first line contains $N$, $M$, and $Q$.

The next $M$ lines contain two integers, $l$ and $r$ ($1 \leq l \leq r \leq N$) — the endpoints of each update.

The next $Q$ lines contain three integers, $l$, $r$, and $k$ ($1 \leq l \leq r \leq N, 1 \leq k \leq r - l + 1$) — the endpoints of each query and the length of the subsequence.

Output Format

Output $Q$ lines. The $i$th line should contain the answer for the $i$th query.

5 3 9
1 5
2 4
3 3
1 5 5
1 5 4
1 5 3
1 5 2
1 5 1
2 5 4
2 5 3
2 5 2
2 5 1

21
13
7
3
1
5
5
3
1

9 1 1
7 9
1 8 8

3

30 1 1
1 30
1 30 30

73741816

Hint

For Sample 1:

After performing the $M$ operations, the string is $10101$.

For the first query, there is only one subsequence of length $5$, $10101$, which is interpreted as $1 \cdot 2^4 + 0 \cdot 2^3 + 1 \cdot 2^2 + 0 \cdot 2^1 + 1 \cdot 2^0 = 21$.

For the second query, there are $5$ unique subsequences of length $4$: $0101$, $1101$, $1001$, $1011$, $1010$. The lexicographically largest subsequence is $1101$, which is interpreted as $1 \cdot 2^3 + 1 \cdot 2^2 + 0 \cdot 2^1 + 1\cdot 2^0 = 13$.

For the third query, the lexicographically largest sequence is $111$, which is interpreted as $7$.

For Sample 3:

Make sure to output the answer modulo $10^9+7$.

SCORING:

• Input 4: $N \leq 10, Q \leq 1000$
• Input 5: $M \leq 10$
• Inputs 6-7: $N, Q \leq 1000$
• Inputs 8-12: $N \leq 2 \cdot 10^5$
• Inputs 13-20: No additional constraints.