B. Dmytro and Bottles

Dmytro has $n$ plastic bottles, each capable of holding exactly $k$ liters of water. The $i$-th bottle currently contains $a_i$ liters of water.

Having recently become aware of the environmental impact of plastic, Dmytro wants to recycle as many bottles as possible. To achieve this, he plans to redistribute the water among the bottles so that no bottle exceeds its capacity of $k$ liters. However, Dmytro prefers to minimize the amount of water he has to pour.

Your task is to help Dmytro determine the minimum number of bottles required to hold all the water and the minimum number of liters that need to be poured.

Note that water from one bottle can be distributed across multiple other bottles. It is not necessary to transfer all the water from one bottle into just one other bottle.

Input

The first line contains two integers $n$ and $k$ ($1\le n\le 10^5$, $1\le k\le 10^4$) — the number of bottles and the maximum capacity of each bottle.

The second line contains $n$ integers $a_1,a_2,\dots ,a_n$ ($0\le a_i\le k$) — the current amount of water in each bottle.

Output

Output a single line with two integers: the number of bottles needed to hold all the water, and the minimum number of liters that need to be poured.

Examples

Note

In the first example, all the water from the 5th bottle can be transferred to the 3rd bottle, and the water from the 1st bottle can be poured into the 6th bottle.

In the second example, all 5 bottles are required, so no pouring is necessary.

In the third example, you can select any bottle and pour 1 liter from it into all the others.