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The integers $1, 2, \dots, 40$ are written on a blackboard. The following operation is then repeated $39$ times. In each repetition, any two numbers, say a and b, currently on the blackboard are erased and a new number $a+b-1$ is written. What will be the number left on the board at the end?

  1. $820$
  2. $821$
  3. $781$
  4. $819$
  5. $780$
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