Andrewid the Android is a galaxy-famous detective. He is now chasing a criminal hiding on the planet Oxa-5, the planet almost fully covered with water.

The only dry land there is an archipelago of n narrow islands located in a row. For more comfort let's represent them as non-intersecting segments on a straight line: island i has coordinates [l_i, r_i], besides, r_i < l_i + 1 for 1 ≤ i ≤ n - 1.

To reach the goal, Andrewid needs to place a bridge between each pair of adjacent islands. A bridge of length a can be placed between the i-th and the (i + 1)-th islads, if there are such coordinates of x and y, that l_i ≤ x ≤ r_i, l_i + 1 ≤ y ≤ r_i + 1 and y - x = a.

The detective was supplied with m bridges, each bridge can be used at most once. Help him determine whether the bridges he got are enough to connect each pair of adjacent islands.

The first line contains integers n (2 ≤ n ≤ 2·10⁵) and m (1 ≤ m ≤ 2·10⁵) — the number of islands and bridges.

Next n lines each contain two integers l_i and r_i (1 ≤ l_i ≤ r_i ≤ 10¹⁸) — the coordinates of the island endpoints.

The last line contains m integer numbers a₁, a₂, ..., a_m (1 ≤ a_i ≤ 10¹⁸) — the lengths of the bridges that Andrewid got.

If it is impossible to place a bridge between each pair of adjacent islands in the required manner, print on a single line "No" (without the quotes), otherwise print in the first line "Yes" (without the quotes), and in the second line print n - 1 numbers b₁, b₂, ..., b_n - 1, which mean that between islands i and i + 1 there must be used a bridge number b_i.

If there are multiple correct answers, print any of them. Note that in this problem it is necessary to print "Yes" and "No" in correct case.