The Last of Us

curly_braces CUET CSE Fest 2022 - Inte...
Limits 2s, 256 MB

Your friend Herok loves Math so much. He is going to write some numbers on some paper. As he is your best friend you know how he writes the numbers one after another. For the first number, he writes a random integer pp, between 1 and nn inclusive. After that for the next numbers, he will choose a number q(1qn)q(1 \leq q \leq n) such that either qq is divisible by the last number he wrote or the last number wrote is divisible by qq. For example, let n=10n=10 and the last number he wrote was 44, the possible values of qq for the next number are 1,2,4,81, 2, 4, 8. Among all the possible options of qq he chooses randomly. He has written kk numbers on some secret paper. You are wondering about what’s the last number he wrote on the paper.

Given the values of nn and kk, for each integer from 11 to nn, you have to print the probability that he wrote that number as the last number. Print the probability modulo 109+710^9+7.

Input

The input consists of 2 space-separated integers n,k(1n,k5000)n, k (1 \leq n,k \leq 5000) described above.

Output

Print nn space-separated integers in a line, for each integer from 11 to nn, the probability that Herok wrote that number as the last number. Print the probability modulo 109+710^9+7.

Samples

InputOutput
2 3
500000004 500000004
InputOutput
1 3
1

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Statistics

75% Solution Ratio
MatrixEarliest, 1M ago
Hamim_Fastest, 0.5s
niaj_pialLightest, 5.7 MB
MatrixShortest, 1439B
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