Queue

Notes

Template in C

Constraints

• 1 ≤ n ≤ 100000
• 1 ≤ q ≤ 1000
• 1 ≤ timei ≤ 50000
• 1 ≤ length of namei ≤ 10
• 1 ≤ Sum of timei ≤ 1000000

Input

n q name1 time1 name2 time2 ... namen timen

In the first line the number of processes n and the quantum q are given separated by a single space.

In the following n lines, names and times for the n processes are given. namei and timei are separated by a single space.

Output

For each process, prints its name and the time the process finished in order.

Example

Input

5 100 p1 150 p2 80 p3 200 p4 350 p5 20

Output

p2 180 p5 400 p1 450 p3 550 p4 800

inputFormat

Input

n q name1 time1 name2 time2 ... namen timen

In the first line the number of processes n and the quantum q are given separated by a single space.

In the following n lines, names and times for the n processes are given. namei and timei are separated by a single space.

outputFormat

Output

For each process, prints its name and the time the process finished in order.

Example

Input

5 100 p1 150 p2 80 p3 200 p4 350 p5 20

Output

p2 180 p5 400 p1 450 p3 550 p4 800

样例

5 100
p1 150
p2 80
p3 200
p4 350
p5 20

p2 180
p5 400
p1 450
p3 550
p4 800

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