A9896 | Case of Fugitive

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 $n$ ( $2<=n<=2·10^{5}$ ) and $m$ ( $1<=m<=2·10^{5}$ ) — the number of islands and bridges.

Next $n$ lines each contain two integers $l_{i}$ and $r_{i}$ ( $1<=l_{i}<=r_{i}<=10^{18}$ ) — the coordinates of the island endpoints.

The last line contains $m$ integer numbers $a_{1},a_{2},...,a_{m}$ ( $1<=a_{i}<=10^{18}$ ) — 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 $b_{1},b_{2},...,b_{n-1}$ , 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.