Rods

A laboratory at a certain company is testing a new material called politoksyparen. During the research an interesting property was discovered: a straight rod made of this material, when heated, lengthens and bends so that it turns into a circular arc whose chord is the rod's original straight shape (this property holds only for rods of very small diameter).

Suppose there are $n$ rods of very small diameter, where the $i$-th rod has initial length $l_i$ ($1 \le l_i \le 100\,000$). When heated, each rod lengthens by $d_i$ ($1 \le d_i \le 100$, with $d_i \le l_i / 2$). Lengths are measured in millimeters.

Write a program that:

• reads from standard input the number of rods $n$ and, for each rod, its length $l_i$ and its increase in length $d_i$;
• for each rod, computes the distance between the midpoint of the chord and the midpoint of the arc after heating (assuming the rod really bends into a circular arc); the answer must be an integer that differs from the exact value by at most $0.5$;
• writes the results to standard output.

The first line contains one positive integer $n$ ($n \le 50\,000$). Each of the next $n$ lines contains two integers separated by a single space: the original length of the rod $l_i$ and its increase in length while heated $d_i$.

Print $n$ lines, each containing one nonnegative integer. The integer on the $i$-th line must equal the distance between the position of the midpoint of the $i$-th rod before and after heating, computed to the required accuracy.