# Pyramid Number

A group of archaeologists have come across a new kind of number pattern while analyzing the hieroglyphs patterns in ‘The not so great pyramid’. They have decided to call these numbers ‘Pyra- mid numbers’. A number n is called a Pyramid number if we can partition n into k positive integers xi (1 ≤ i ≤ k) such that ∑k 1 =1.Forexample,1=1+1 i=1xi 22 So, 4 (2 + 2) is a Pyramid number. A number n is called a Strictly Pyramid number if we can partition n into k distinct positive integers xi (1 ≤ i ≤ k) such that ∑k 1 =1.Forexample,1=1+1+1 Here, 11 (2 + 3 + 6) is Strictly Pyramid whereas in the above example, 4 is Pyramid but not Strictly Pyramid. Given two positive integers a & b, find the number of Strictly Pyramid numbers between a & b (inclusive). Input The first line of the input file will contain an integer T (T ≤ 100), the number of test cases. Each of the following T lines will be consisting of 2 integers a & b (1 ≤ a, b ≤ 1000000). Output For each test case, print an integer which is the number of Strictly Pyramid numbers between a & b (inclusive). Sample Input 5 1 10 1 11 1 100 70 80 110 120 Sample Output 1 2 53 8 11 i=1 xi 2 3 6