5343: Square Equation Roots
内存限制：256 MB
时间限制：2 S
标准输入输出
题目类型：传统
评测方式：文本比较
上传者：
提交：5
通过：1
题目描述
E. Square Equation Roots
time limit per test
5 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output
A schoolboy Petya studies square equations. The equations that are included in the school curriculum, usually look simple:
x2+2bx+c=0where b, c are natural numbers. Petya noticed that some equations have two real roots, some of them have only one root and some equations don't have real roots at all. Moreover it turned out that several different square equations can have a common root.
Petya is interested in how many different real roots have all the equations of the type described above for all the possible pairs of numbers b and c such that 1≤b≤n, 1≤c≤m. Help Petya find that number.
x2+2bx+c=0where b, c are natural numbers. Petya noticed that some equations have two real roots, some of them have only one root and some equations don't have real roots at all. Moreover it turned out that several different square equations can have a common root.
Petya is interested in how many different real roots have all the equations of the type described above for all the possible pairs of numbers b and c such that 1≤b≤n, 1≤c≤m. Help Petya find that number.
Input
The single line contains two integers n and m. (1≤n,m≤5000000).
Output
Print a single number which is the number of real roots of the described set of equations.
Examples
Input
3 3
Output
12
Input
1 2
Output
1
Note
In the second test from the statement the following equations are analysed: b=1, c=1: x2+2x+1=0; The root is x=-1
b=1, c=2: x2+2x+2=0; No roots
Overall there's one root
In the second test the following equations are analysed:
b=1, c=1: x2+2x+1=0; The root is x=-1
b=1, c=2: x2+2x+2=0; No roots
b=1, c=3: x2+2x+3=0; No roots
b=2, c=1: x2+4x+1=0; The roots are
b=2, c=2: x2+4x+2=0; The roots are
b=2, c=3: x2+4x+3=0; The roots are x1=-3,x2=-1
b=3, c=1: x2+6x+1=0; The roots are
b=3, c=2: x2+6x+2=0; The roots are
b=3, c=3: x2+6x+3=0; The roots are
Overall there are 13 roots and as the root -1 is repeated twice, that means there are 12 different roots. 输入样例 复制
输出样例 复制