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```import java.util.Scanner;

public class MagneticMaterials {

// A constant for the magnetic constant k
public static final double k = 1e-7;

// A method to calculate the magnetic force between two objects
public static double magneticForce(double m1, double m2, double d) {
return k * m1 * m2 / (d * d);
}

// A method to find the point of balance between two magnetic materials
public static double pointOfBalance(double x1, double x2, double m1, double m2) {
// Use binary search to find the point where the forces are equal
double low = x1;
double high = x2;
double mid = (low + high) / 2;
double error = 1e-9; // The maximum error allowed
while (Math.abs(low - high) > error) {
// Calculate the forces at the mid point
double f1 = magneticForce(m1, m2, mid - x1);
double f2 = magneticForce(m2, m1, x2 - mid);
// If the forces are equal, return the mid point
if (Math.abs(f1 - f2) < error) {
return mid;
}
// If the force from the left is greater, move the low point to the right
if (f1 > f2) {
low = mid;
}
// If the force from the right is greater, move the high point to the left
if (f2 > f1) {
high = mid;
}
// Update the mid point
mid = (low + high) / 2;
}
// Return the approximate point of balance
return mid;
}

public static void main(String[] args) {
// Create a scanner object to read input
Scanner sc = new Scanner(System.in);
// Read the number of test cases
int t = sc.nextInt();
// Loop through each test case
for (int i = 1; i <= t; i++) {
// Read the number of magnetic materials
int n = sc.nextInt();
// Create arrays to store the x coordinates and magnetic moments of the magnetic materials
double[] x = new double[n];
double[] m = new double[n];
// Read the x coordinates and magnetic moments of the magnetic materials
for (int j = 0; j < n; j++) {
x[j] = sc.nextDouble();
m[j] = sc.nextDouble();
}
// Print the case number
System.out.print("#" + i + " ");
// Loop through each pair of adjacent magnetic materials and find the point of balance
for (int j = 0; j < n - 1; j++) {
double p = pointOfBalance(x[j], x[j + 1], m[j], m[j + 1]);
// Print the point of balance with 10 digits after the decimal point
System.out.printf("%.10f ", p);
}
// Print a new line after each case
System.out.println();
}
// Close the scanner object
sc.close();
}
}
```