#include <stdio.h>
#include <math.h>
#include <ctype.h>

// Calculate AMA consultation price
double calculate_ama_price(int t, int n) {
    const double base_price = 5.0;      // Base price 5 dollars
    const double time_exponent = 1.3;   // Time exponent
    const double topic_discount = 0.9;  // Multi-topic discount coefficient
    
    // Calculate time coefficient
    double time_factor = pow(t, time_exponent);
    
    // Calculate topic coefficient
    double topic_factor = (n == 1) ? 1.0 : (topic_discount * n);
    
    // Calculate total price and round to two decimal places
    double total_price = base_price * time_factor * topic_factor;
    total_price = round(total_price * 100) / 100;
    
    return total_price;
}

// Get positive integer input
int get_positive_input(const char* prompt) {
    int value;
    char ch;
    
    while(1) {
        printf("%s", prompt);
        
        // Check if integer was read successfully
        if(scanf("%d", &value) != 1) {
            // Clear erroneous input
            while((ch = getchar()) != '\n' && ch != EOF);
            printf("Invalid input, please enter a positive integer\n");
            continue;
        }
        
        // Check if positive
        if(value <= 0) {
            printf("Please enter an integer greater than 0\n");
            continue;
        }
        
        // Clear remaining characters in input buffer
        while((ch = getchar()) != '\n' && ch != EOF);
        
        return value;
    }
}

int main() {
    printf("=== AMA Consultation Price Calculator ===\n");
    
    // Get user input
    int hours = get_positive_input("Enter consultation time (hours): ");
    int topics = get_positive_input("Enter number of topics: ");
    
    // Calculate price
    double price = calculate_ama_price(hours, topics);
    
    // Display result
    printf("\n=== Calculation Result ===\n");
    printf("Consultation time: %d hours\n", hours);
    printf("Number of topics: %d\n", topics);
    printf("Total price: $%.2f\n", price);
    
    // Display calculation formula
    printf("\nCalculation formula: \n");
    printf("5 × %d^1.3 × ", hours);
    if(topics == 1) {
        printf("1 = $%.2f\n", price);
    } else {
        printf("0.9 × %d = $%.2f\n", topics, price);
    }
    
    return 0;
}