def birthday(s, d, m):
    selected_sum = sum(s[:m])
    num_of_ways = 0
    
    if selected_sum == d:
        num_of_ways += 1
    
    for i in range(len(s) - m):    
        selected_sum += s[i + m] - s[i]
        
        if selected_sum == d:
            num_of_ways += 1
    
    return num_of_ways