402815: GYM100886 J Sockets

Valera has only one electrical socket in his flat. He also has m devices which require electricity to work. He's got n plug multipliers to plug the devices, the i-th plug multiplier has a_i sockets.

A device or plug multiplier is supplied with electricity if it is either plugged into the electrical socket, or if it is plugged into some plug multiplier which is supplied with electricity.

For each device j, Valera knows the safety value b_j which is the maximum number of plug multipliers on the path between the device and the electrical socket in his flat. For example, if b_j = 0, the device should be directly plugged into the socket in his flat.

What is the maximum number of devices Valera could supply with electricity simultaneously? Note that all devices and plug multipliers take one socket to plug, and that he can use each socket to plug either one device or one plug multiplier.

The first line contains two space-separated integers n and m (1 ≤ n, m ≤ 2·10⁵), the number of plug multipliers and the number of devices correspondingly.

The second line contains n space-separated integers a₁, a₂, ..., a_n (2 ≤ a_i ≤ 2·10⁵). Here, the number a_i stands for the number of sockets on the i-th plug multiplier.

The third line contains m space-separated integers b₁, b₂, ..., b_m (0 ≤ b_j ≤ 2·10⁵). Here, the number b_j stands for the safety value of the j-th device.

Print a single integer: the maximum number of devices that could be supplied with electricity simultaneously.

3 5
3 2 2
1 2 2 1 1

4

3 3
2 2 2
1 2 2

3