An arcade's bonus-token conveyor carries a line of n multiplier tokens, each showing a positive integer value, moving past a fusion press in order. The press makes exactly one pass over the belt, left to right, and works like this: it opens a new combined token equal to the value of the first token on the belt. For every following token, in order, the press checks whether multiplying that token's value into the currently open combined token would keep the combined token's value at or below the belt's safety ceiling C. If so, it fuses the token in (the combined token's value becomes that product) and moves on. If not, it seals the currently open combined token exactly as it is, opens a brand-new combined token starting from that following token's value, and continues. After the last token has been processed, the press seals whatever combined token is still open.

Report the values of the sealed combined tokens, in the order they were sealed.

Input format

Line 1: two integers n C. Line 2: n integers a_1 a_2 ... a_n, the multiplier tokens in belt order.

Output format

The sealed combined-token values, space-separated, in order.

Constraints

• 1 <= n <= 200000
• 1 <= C <= 1000000000
• 1 <= a_i <= 1000000000

4 5
2 2 2 2

4 4

5 10
3 2 4 1 5

6 4 5