Concert

In Bitland, the long-awaited concert of the famous local band Bitlai is about to begin. $N$ spectators have gathered to watch it, and the hall is arranged so that they stand in a single line, one directly behind another: spectator $1$ stands right at the stage, spectator $2$ stands behind spectator $1$, spectator $3$ behind spectator $2$, and so on. The spectator at position $i$ has height $u_i$ (Bitland meters). A spectator can see the stage only if every spectator standing in front of them is strictly shorter.

The organizers did not plan for this and have only $K$ chairs to hand out, each exactly $1$ Bitland meter tall. A chair can hold only one spectator, and each spectator may receive at most one chair. When a spectator stands on a chair, their height increases by $1$ Bitland meter. As a result that spectator may become able to see the stage, but they may also block the view of the spectators standing behind them.

Find the maximum number of spectators who can see the stage if the chairs are distributed optimally.

The first line contains two space-separated integers: the number of spectators $N$ and the number of chairs $K$.

The second line contains $N$ space-separated integers $u_i$ — the heights of the spectators in the order they stand in the hall.

Print a single integer — the maximum number of spectators who can see the concert when the chairs are distributed optimally.

• $1 \le K \le N \le 100000$
• $1 \le u_i \le 1000000$ ($1 \le i \le N$)