The Hispaniola has finally approached Treasure Island! The pirates’ boat has already set off towards the island and has drifted away from the ship by D feet. Jim’s boat has just been launched into the water and is at the same point as the ship.

For the next n seconds, both boats will move in a straight line towards the island. Jim knows exactly that in the i-th second, the pirates’ boat will move towards the island by b_i feet. At the same time, in the i-th second, Jim’s boat can move towards the island by any integer number of feet from 0 to a_i at Jim’s discretion. Assume that during each second both boats move uniformly.

Jim wants to overtake the pirates’ boat as soon as possible so that after that the pirates will never catch up with Jim. Formally, let t (1 ≤ t ≤ n) be the smallest second number such that at the end of it Jim’s boat is strictly closer to the island than the pirates’ boat. Jim wants to ensure that starting from this moment and until the end of the n-th second, his boat is strictly closer to the island than the pirates’ boat. Out of all possible t, he wants to choose the smallest one.

However, Jim does not know the distance D exactly. He has q assumptions d₁, d₂, …, d_q about what D could be. He wants to know the smallest possible number t for each of his assumptions.

The first line contains two integers n and q — the number of seconds and the number of Jim’s assumptions (1 ≤ n ≤ 10⁵, 1 ≤ q ≤ 10⁵).

The second line contains n integers a₁, a₂, …, a_n — the maximum possible distances that Jim’s boat can travel in each second (0 ≤ a_i ≤ 10⁹).

The third line contains n integers b₁, b₂, …, b_n — the distances that the pirates’ boat will travel (0 ≤ b_i ≤ 10⁹).

The fourth line contains q integers d₁, d₂, …, d_q — the assumed initial distances of the pirates’ boat from the ship (1 ≤ d_i ≤ 10⁹).

In q lines, output one integer — the answer to each of Jim’s assumptions.

If Jim can overtake the pirates at the end of second t such that the pirates will never catch him, output the number t (1 ≤ t ≤ n). Out of all suitable numbers t, output the smallest one. If Jim’s plan is impossible to execute, output −1.