CodeSprint2 - Picking Cards

# A python implementation of a solution to the Picking Cards
# problem for Codesprint 2.
# Author: Kevin Tham

def solve(numCards, sortedCards, numPickedUp):
    # O(n): Calculate a table to store number of cards less than a particular card number
    numLessThanOrE = {}
    for index in xrange(numCards):
        cardsPicked = index+1
        numLessThanOrE[sortedCards[index]]= cardsPicked

    # O(n): Fill in missing values
    lastValue = 0
    for index in xrange(numCards):
        if numLessThanOrE.has_key(index):
            lastValue = numLessThanOrE[index]
        else:
            numLessThanOrE[index] = lastValue

    # O(n): Calculate the number of possibilities
    totalPossibilities = 1
    for cardsPicked in xrange(numCards):
        possibleCards = numLessThanOrE[cardsPicked] - cardsPicked
        if possibleCards >= 0:
            totalPossibilities = (totalPossibilities * possibleCards) % 1000000007
    return totalPossibilities

def main():
    numCases = int(raw_input())
    for eachCase in range(numCases):
        numCards = int(raw_input())
        sortedCards = sorted(map(int, raw_input().split()))
        print solve(numCards, sortedCards, 0)

if __name__ == '__main__':
    main()