Write a Python program to implement stemming for a given sentence using NLTK.

import nltk
from nltk.stem import PorterStemmer
from nltk.tokenize import word_tokenize
nltk.download('punkt')
stemmer = PorterStemmer()
sentence = "The leaves are falling and the cats are running swiftly"
words = word_tokenize(sentence)
stemmed_words = [stemmer.stem(word) for word in words]
print("Original Words:", words)
print("Stemmed Words:", stemmed_words)
# Original Words: ['The', 'leaves', 'are', 'falling', 'and', 'the', 'cats', 'are', 'running', 'swiftly']
# Stemmed Words: ['the', 'leav', 'are', 'fall', 'and', 'the', 'cat', 'are', 'run', 'swiftli']