## CLEAR - Clear Numbers

English | Vietnamese |

Bom has just found a definition of **clear numbers** as the following: for each positive integer n, we form another number by summing the squares of the digits of n. We repeat this procedure. If at some step, we obtain the number 1 then n is called a **clear number**. For example, for n=19, we have:

19 → 82 (= 1^{2} +9^{2}) → 68 → 100 → 1

Thus, 19 is a clear number.

Not all numbers are clear numbers. For example, for n=12, we have:

12 → 5 → 25 → 29 → 85 → 89 → 145 → 42 → 20 → 4 → 16 → 37 → 58 → 89 → 145

Bom is very interested in this definition of clear numbers. He issued a challenge to the landlord: given a positive integer n, find S(n), the clear number succeeding n, i.e. S(n) is the minimum clear number greater than n. However, this question is so easy for the landlord that he challenged Bom with another problem: given two positive integers n and m (1 ≤ n, m ≤ 10^{15}), find the number S^{m}(n)=S(S(…S(n) )) which is the m^{th} clear number succeeding n.

Please help Bom to solve the task!

### Input

The first line contains t (0 < t ≤ 20) , the number of test cases.

Each line in the next t lines contains two positive integers n and m.

### Output

Print t lines, each line contains the result of the corresponding test case.

### Example

Input2 18 1 1 145674807Output19 1000000000

### Notes

There are 50% of the test cases in which 1 ≤ n, m ≤ 10^{7}.

Added by: | Jimmy |

Date: | 2009-07-16 |

Time limit: | 0.200s |

Source limit: | 50000B |

Memory limit: | 1536MB |

Cluster: | Cube (Intel G860) |

Languages: | All except: ERL JS-RHINO NODEJS PERL6 VB.NET |

Resource: | VNOI Marathon 2009 Round 2 Problem Setter: Đỗ Đức Đông |