F. Kilani's Startup
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

After a long training session and (the tragic loss of an HDMI cable), Kilani needed something to cheer himself up. He found the legendary 7aleeb Baladna in a vending machine and buy it Seeing his teammates rushing toward the machine, he sees an opportunity so he bought all available milk and decided to resell the milk with one strict rule:

ElDain Mamnoo3 wel 3atb Marfoo3 (No debt. No exceptions.)

There are $$$n$$$ guys standing in a line. Kilani has $$$m$$$ milk bottles, each with a fixed price. The $$$i$$$-th guy has $$$a_i$$$ money, and the $$$j$$$-th bottle has price $$$b_j$$$.

Each guy, in order from $$$1$$$ to $$$n$$$, wants to buy exactly one bottle. A guy will buy the most expensive available bottle whose price does not exceed his money. Each bottle can be sold at most once. If a guy cannot afford any available bottle, he leaves without buying anything.

Your task is to determine the number of guys who cannot buy any bottle and output their indices in increasing order.

Input

The first line contains two integers $$$n$$$ and $$$m$$$ ($$$1 \le n, m \le 2 \cdot 10^5, (m \le n)$$$) — the number of guys and the number of milk bottles respectively.

The second line contains $$$n$$$ integers $$$a_1, a_2, \dots, a_n$$$ ($$$1 \le a_i \le 10^9$$$) — the amount of money the $$$i$$$-th guy has.

The third line contains $$$m$$$ integers $$$b_1, b_2, \dots, b_m$$$ ($$$1 \le b_j \le 10^9$$$) — the price of the $$$j$$$-th milk bottle.

Output

Print in the first line a single integer $$$k$$$, the number of guys who cannot buy any bottle.

In the second line, print $$$k$$$ integers, the indices of those guys in increasing order. If $$$k = 0$$$, print a single line containing $$$0$$$.

Examples
Input
5 3
10 4 8 3 15
5 7 12
Output
2
2 4
Input
4 4
5 6 7 8
1 2 3 4
Output
0