5192：Building Blocks Ⅱ

LeLe is playing with blocks again.He wants to rebuild the blocks which he built yesterday.

LeLe wants to build piles which contains consecutive $W$ piles with the same height and the height is not shorter than $H$.

LeLe already put all of his blocks in these piles, which means he can not add any blocks into them.Besides, he can move a block from one pile to another or a new one，but not the position betweens two piles already exists.For instance,after one move,"3 2 3" can become "2 2 4" or "3 2 2 1",but not "3 1 1 3".

You are request to calculate the minimum blocks should LeLe move and the height.

There are multiple test cases, about $100$ cases.

The first line of input contains three integers $n,W,H(1 \leq n,W,H \leq 50000)$.$n$ indicate $n$ piles blocks.

For the next line ,there are $n$ integers $A_1,A_2,A_3,……,A_n$ indicate the height of each piles.$(1 \leq A_i \leq 50000)$.

The height of a block is 1.

For each case, output two integers,the first one is $h$ (indicate the height of W piles),the second one is the minimum number of blocks should LeLe move.

If there are multiple solutions output the maximal $h$.

If there is no solution, output "-1" (without quotes).