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

见题面

见题面