Problem Description

Given house positions on a line and WiFi routers with their ranges, check if every house gets WiFi coverage. Return "YES" if all houses are covered, "NO" otherwise.

Input Format

First line: n m (houses, routers). Second line: n house positions. Third line: m router positions. Fourth line: m router ranges.

Output Format

"YES" if all houses are covered, "NO" otherwise.

Constraints

• 1 ≤ n, m ≤ 1000

• 0 ≤ positions ≤ 10^6

• 1 ≤ router ranges ≤ 10^6

• House covered if within range of any router

• Range is inclusive on both sides

Sample Input/Output

Explanation

Houses at [1,5,9]. Routers at [3,7] with ranges [3,2]. Router 1 covers [0,6], Router 2 covers [5,9]. All houses covered.