SP8327 PROGPROG - Progressive progressions

An arithmetic progression is a sequence of numbers a $ _{1} $ , a $ _{2} $ ,... a $ _{n} $ such that a $ _{i+1} $ -a $ _{i} $ is equal for all 0 Now consider a sequence of arithmetic progressions A $ _{1} $ = (a $ _{1,1} $ , a $ _{1,2} $ ,... a $ _{1,n1} $ ), A $ _{2} $ = (a $ _{2,1} $ , a $ _{2,2} $ ,... a $ _{2,n2} $ ),... A $ _{k} $ = (a $ _{k,1} $ , a $ _{k,2} $ ,... a $ _{k,nk} $ ) A progressive progression is such a sequence with the additional properties that: - a $ _{i,ni} $ = a $ _{i+1,1} $ for 1 - c $ _{i} $ , the common difference of A $ _{i} $ , is a positive factor of a $ _{i,1} $ for 1 - c $ _{i} $ 1 for 1 - k >= 1 Find the number of progressive progressions such that a $ _{1,1} $ =1 and a $ _{k,nk} $ = N. As this number can be quite large, output it modulo 100000007.

The first line of input contains T (

For each testcase, output modulo 100000007 the number of progressive progressions such that a $ _{1,1} $ =1 and a $ _{k,nk} $ = N