"Piku", also starring Deepika Padukone in the titular role, is about her relationship with her father (Bachchan), who spends most of his time obsessing over age-related issues.
Irrfan forms the third wheel of the story.
Shoojit now feels the megastar's chemistry with Irrfan is one of the highlights of the movie.
"I tell everyone Irrfan is the only international star we have. I was sceptical the first day he and Mr Bachchan met on the set, it was a Robert De Niro and Al Pacino moment for me.
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The director shared that by the end of the film, Irrfan became an admirer of Bachchan's style of working.
For Shoojit, "Piku" became a one-of-its-kind experience as the film's set was home to three different schools of acting.
"All three of them are absolutely poles apart. Mr Bachchan will constantly do rehearsals and then he will go for a take and that will be the final take. Deepika will do rehearsals but while doing that she will try to grab her movements, performances.