How to make a timer program in Python

Here is my goal: To make a small program (text based) that will start with a greeting, print out a timer for how long it has been since the last event, and then a timer for the event. I have used this code to start out with trying to figure out a timer, but my first problem is that the timer keeps repeating on a new line with each new second. How do I get that to stop? Also, this timer seems to lag behind actual seconds on the clock.

import os
import time


s=0
m=0

while s<=60:
    os.system('cls')
    print (m, 'Minutes', s, 'Seconds')
    time.sleep(1)
    s+=1
    if s==60:
        m+=1
        s=0