[Python] Understanding change-making algorithm

I was looking for a good solution to the Change-making problem and I found this code(Python):

target = 200
coins = [1,2,5,10,20,50,100,200]
ways = [1]+[0]*target
for coin in coins:
for i in range(coin,target+1):
ways+=ways[i-coin]
print(ways[target])


I have no problems understanding what the code literally does,but I can't understand WHY it works. Anyone can help?

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