------
## 最终结论
```python
def subarraysDivByK(A, K):
    prefix_sum_count = {0: 1}  # Initialize dictionary with 0 remainder count
    prefix_sum = 0
    count = 0
    
    for num in A:
        prefix_sum += num  # Calculate current prefix sum
        remainder = prefix_sum % K  # Update the remainder
        
        if remainder < 0:  # Handle negative remainders
            remainder += K
        
        # Check if this remainder has been seen before
        if remainder in prefix_sum_count:
            count += prefix_sum_count[remainder]  # Increase count by the number of times this remainder has appeared
            prefix_sum_count[remainder] += 1  # Increment the count of this remainder
        else:
            prefix_sum_count[remainder] = 1  # Initialize this remainder in the dictionary

    return count

# Example usage:
A = [4,5,0,-2,-3,1]
K = 5
print(subarraysDivByK(A, K))  # Output: 7
```