NY10E - Non-Decreasing Digits


A number is said to be made up of non-decreasing digits if all the digits to the left of any digit is less than or equal to that digit.For example, the four-digit number 1234 is composed of digits that are non-decreasing.  Some other four-digit numbers that are composed of non-decreasing digits are 0011, 1111, 1112, 1122, 2223.  As it turns out, there are exactly 715 four-digit numbers composed of non-decreasing digits.
 
Notice that leading zeroes are required: 0000, 0001, 0002 are all valid four-digit numbers with non-decreasing digits.
 
For this problem, you will write a program that determines how many such numbers there are with a specified number of digits.

Input

The first line of input contains a single integer P, (1 ≤ P ≤ 1000), which is the number of data sets that follow.  Each data set is a single line that contains the data set number, followed by a space, followed by a decimal integer giving the number of digits N, (1 ≤ N ≤ 64).

Output

For each data set there is one line of output.  It contains the data set number followed by a single space, followed by the number of N digit values that are composed entirely of non-decreasing digits.

Example

Input:
3
1 2
2 3
3 4

Output:
1 55
2 220
3 715

hide comments
it_nyx: 2021-06-05 12:55:14

Easy, but a very nice exercise for beginners in DP that I can recommend to my students. Thx!

yash5507: 2020-12-31 15:39:37

AC in one GO! ( Simplest Digit Dp)

singhgur_123: 2020-08-11 18:39:28

Mayb for i digit no place j=0 to 9 at last place and count no i-1 no satisfying the condition
i am new to spoj i am really sorry if posting hints like this is not allowed

berserkk: 2020-08-02 07:00:50

AC in one go

robosapien: 2020-07-13 00:05:24

Observing sample cases, you can notice a formula.
But i guess i should look up how to solve it using dp and not observations :P

ujjwal_jain10: 2020-06-25 09:37:35

AC in 69th go

manish_thakur: 2020-05-20 09:05:55

who puts input format like this? :(

abhishek_2002: 2020-05-15 12:44:19

AC aaya hi ni....

amansahu112: 2020-04-30 12:57:38

solve some maths . there is a formula hidden

saketvajp_123: 2020-04-18 06:46:50

AC in two go !!


Added by:John Mario
Date:2011-03-22
Time limit:1s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ASM64
Resource:ACM Greater New York Regionals 2010