Problem Statement

There are $N$ towns, numbered $1,2,\ldots,N$, arranged in a line in this order.

There are $N-1$ roads connecting adjacent towns: road $j\,(1 \leq j \leq N-1)$ connects towns $j$ and $j+1$. For each road $j$, you can set a strength $w_j$ (an integer that may be negative).

When a person travels along a road, their stamina changes. Specifically, if a person with stamina $x$ travels along road $j$, their stamina becomes $x + w_j$.

There are $M$ people who will now move between these towns.

Person $i\,(1 \le i \le M)$ starts with stamina $0$ at town $S_i$ and travels to town $T_i$ via the shortest path. It is guaranteed that $|S_i - T_i| > 1$. Also, $(S_i, T_i) \neq (S_j, T_j)$ if $i \neq j$.

Person $i$’s requirement is as follows:

When departing Town $S_i$ and when arriving at Town $T_i$, their stamina should be exactly $0$. At every other town, their stamina should always be a positive integer.

Assume that there are no changes to stamina other than those due to traveling along roads as described above.

Process $Q$ queries. For the $k$-th query $(1 \le k \le Q)$, if it is possible to set the strengths of the roads so that the requirements of all people $L_k, L_k + 1, \ldots, R_k$ are satisfied, print Yes; otherwise, print No.

Constraints

• $3 \le N \le 4 \times 10^5$
• $1 \le M \le 2 \times 10^5$
• $1 \le Q \le 2 \times 10^5$
• $1 \le S_i, T_i \le N$
• $|S_i - T_i| > 1$
• $(S_i, T_i) \neq (S_j, T_j)\,(i \neq j)$
• $1 \le L_k \le R_k \le M$
• All input values are integers.

Input

The input is given from Standard Input in the following format:

N M Q
S_1 T_1
S_2 T_2
\vdots
S_M T_M
L_1 R_1
L_2 R_2
\vdots
L_Q R_Q

Output

Print $Q$ lines.

The $k$-th line should contain Yes if there is a way to set the strengths of the roads so that the requirements of all people $L_k, L_k + 1, \ldots, R_k$ are satisfied, and No otherwise.