Jewels

There are N jewels, numbered 1 to N. The color of these jewels are represented by integers between 1 and K (inclusive), and the color of Jewel i is C_i. Also, these jewels have specified values, and the value of Jewel i is V_i.

Snuke would like to choose some of these jewels to exhibit. Here, the set of the chosen jewels must satisfy the following condition:

• For each chosen jewel, there is at least one more jewel of the same color that is chosen.

For each integer x such that 1 \leq x \leq N, determine if it is possible to choose exactly x jewels, and if it is possible, find the maximum possible sum of the values of chosen jewels in that case.

Constraints

• 1 \leq N \leq 2 \times 10^5
• 1 \leq K \leq \lfloor N/2 \rfloor
• 1 \leq C_i \leq K
• 1 \leq V_i \leq 10^9
• For each of the colors, there are at least two jewels of that color.
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

N K C_1 V_1 C_2 V_2 : C_N V_N

Output

Print N lines. In the i-th line, if it is possible to choose exactly i jewels, print the maximum possible sum of the values of chosen jewels in that case, and print -1 otherwise.

Examples

Input

5 2 1 1 1 2 1 3 2 4 2 5

Output

-1 9 6 14 15

Input

5 2 1 1 1 2 2 3 2 4 2 5

Output

-1 9 12 12 15

Input

8 4 3 2 2 3 4 5 1 7 3 11 4 13 1 17 2 19

Output

-1 24 -1 46 -1 64 -1 77

Input

15 5 3 87 1 25 1 27 3 58 2 85 5 19 5 39 1 58 3 12 4 13 5 54 4 100 2 33 5 13 2 55

Output

-1 145 173 285 318 398 431 491 524 576 609 634 653 666 678

inputFormat

input are integers.

Input

Input is given from Standard Input in the following format:

N K C_1 V_1 C_2 V_2 : C_N V_N

outputFormat

Output

Print N lines. In the i-th line, if it is possible to choose exactly i jewels, print the maximum possible sum of the values of chosen jewels in that case, and print -1 otherwise.

Examples

Input

5 2 1 1 1 2 1 3 2 4 2 5

Output

-1 9 6 14 15

Input

5 2 1 1 1 2 2 3 2 4 2 5

Output

-1 9 12 12 15

Input

8 4 3 2 2 3 4 5 1 7 3 11 4 13 1 17 2 19

Output

-1 24 -1 46 -1 64 -1 77

Input

15 5 3 87 1 25 1 27 3 58 2 85 5 19 5 39 1 58 3 12 4 13 5 54 4 100 2 33 5 13 2 55

Output

-1 145 173 285 318 398 431 491 524 576 609 634 653 666 678

样例

8 4
3 2
2 3
4 5
1 7
3 11
4 13
1 17
2 19

-1
24
-1
46
-1
64
-1
77

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