Walf's clothes have ~N~ possible colors, labelled from ~1~ to ~N~. His top clothing rack has ~N~ hats, the ~i~-th hat having a color of ~h_i~. His bottom clothing rack has ~N~ shirts, the ~i~-th shirt having a color of ~s_i~. No two hats have the same color and no two shirts have the same color.

The colors of hats on the rack are given by ~h_1, h_2, \dots, h_N~ and color of his shirts are given by ~s_1, s_2, \dots, s_N~. These values are fixed and regardless of what Walf wears, his racks will reset to this state at the end of the day.

Each morning, Walf picks a hat and a shirt to wear (for obvious reasons, he only wears blue jeans). To help him decide, his friend Fax restricts his hat choices to ~h_a, h_{a + 1}, \dots, h_{b - 1}, h_b~ and his shirt choices to ~s_c, s_{c + 1}, \dots, s_{d - 1}, h_d~. The values of ~a~, ~b~, ~c~, and ~d~ change from day to day.

There are ~D~ days in total. For each day, output if it's possible that Walf wears the same color hat and shirt. More formally, output if there's some ~a \leq x \leq b~ and ~c \leq y \leq d~ such that ~h_x = s_y~.

Constraints

• ~N, D \leq 100\ 000~
• ~1 \leq h_i, s_i \leq N~
• The values of ~h_i~ are all unique
• The values of ~s_i~ are all unique
• ~1 \leq a \leq b \leq N~
• ~1 \leq c \leq d \leq N~

Input Specification

The first line of input will contain two numbers, ~N~ and ~D~.

The second line of input will contain ~N~ numbers, the ~i~th number is ~h_i~.

The third line of input will contain ~N~ numbers, the ~i~th number is ~s_i~.

The next ~D~ lines will contain 4 numbers each, each line containing the values of ~a~, ~b~, ~c~, and ~d~ for that day.

Output Specification

Output one line with ~D~ characters. The ~j~-th character should be Y if Walf can wear the same color hat and shirt on Day ~j~ and N if he can't.

Sample Input

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

Sample Output

YYN