There live square people in a square country. Everything in this country is square also. Thus, the Square Parliament has passed a law about a land. According to the law each citizen of the country has a right to buy land. A land is sold in squares, surely. Moreover, a length of a square side must be a positive integer amount of meters. Buying a square of land with a side a one pays a2 quadrics (a local currency) and gets a square certificate of a landowner.
One citizen of the country has decided to invest all of his N quadrics into the land. He can, surely, do it, buying square pieces 1 × 1 meters. At the same time the citizen has requested to minimize an amount of pieces he buys: "It will be easier for me to pay taxes," — he has said. He has bought the land successfully.
Your task is to find out a number of certificates he has gotten.
The only line contains a positive integer N ≤ 1015 , that is a number of quadrics that the citizen has invested.
The only line contains a number of certificates that he has gotten.
This problem is the same as “Square country
” but with bigger limitations.
Problem Author: Prepared by Fyodor Menshikov, special thanks to Svyatoslav Demidov