Package for this problem was not updated by the problem writer or Codeforces administration after we’ve upgraded the judging servers. To adjust the time limit constraint, solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then value 800 ms will be displayed and used to determine the verdict.

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ACM-ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

D. Horse Races

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputPetya likes horse racing very much. Horses numbered from *l* to *r* take part in the races. Petya wants to evaluate the probability of victory; for some reason, to do that he needs to know the amount of nearly lucky horses' numbers. A nearly lucky number is an integer number that has at least two lucky digits the distance between which does not exceed *k*. Petya learned from some of his mates from Lviv that lucky digits are digits 4 and 7. The distance between the digits is the absolute difference between their positions in the number of a horse. For example, if *k* = 2, then numbers 412395497, 404, 4070400000070004007 are nearly lucky and numbers 4, 4123954997, 4007000040070004007 are not.

Petya prepared *t* intervals [*l*_{i}, *r*_{i}] and invented number *k*, common for all of them. Your task is to find how many nearly happy numbers there are in each of these segments. Since the answers can be quite large, output them modulo 1000000007 (10^{9} + 7).

Input

The first line contains two integers *t* and *k* (1 ≤ *t*, *k* ≤ 1000) — the number of segments and the distance between the numbers correspondingly. Next *t* lines contain pairs of integers *l*_{i} and *r*_{i} (1 ≤ *l* ≤ *r* ≤ 10^{1000}). All numbers are given without the leading zeroes. Numbers in each line are separated by exactly one space character.

Output

Output *t* lines. In each line print one integer — the answer for the corresponding segment modulo 1000000007 (10^{9} + 7).

Examples

Input

1 2

1 100

Output

4

Input

1 2

70 77

Output

2

Input

2 1

1 20

80 100

Output

0

0

Note

In the first sample, the four nearly lucky numbers are 44, 47, 74, 77.

In the second sample, only 74 and 77 are in the given segment.

Codeforces (c) Copyright 2010-2017 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Jun/25/2017 15:10:16 (c3).

Desktop version, switch to mobile version.

User lists

Name |
---|