B. Angry Monk

To celebrate his recovery, k1o0n has baked an enormous 𝑛 metres long potato casserole.

Turns out, Noobish_Monk just can't stand potatoes, so he decided to ruin k1o0n's meal. He has cut it into 𝑘 pieces, of lengths 𝑎1,𝑎2,…,𝑎𝑘 meters.

k1o0n wasn't keen on that. Luckily, everything can be fixed. In order to do that, k1o0n can do one of the following operations:

• Pick a piece with length 𝑎𝑖≥2 and divide it into two pieces with lengths 1 and 𝑎𝑖−1. As a result, the number of pieces will increase by 1;
• Pick a slice 𝑎𝑖 and another slice with length 𝑎𝑗=1 (𝑖≠𝑗) and merge them into one piece with length 𝑎𝑖+1. As a result, the number of pieces will decrease by 1.

Help k1o0n to find the minimum number of operations he needs to do in order to merge the casserole into one piece with length 𝑛.

For example, if 𝑛=5, 𝑘=2 and 𝑎=[3,2], it is optimal to do the following:

1. Divide the piece with length 2 into two pieces with lengths 2−1=1 and 1, as a result 𝑎=[3,1,1].
2. Merge the piece with length 3 and the piece with length 1, as a result 𝑎=[4,1].
3. Merge the piece with length 4 and the piece with length 1, as a result 𝑎=[5].