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

见题面

见题面