Documentary “Red Army,” premiering this week at Cannes, shows Russia doesn’t just infect Ukraine citizens. Its political disease also infects the athletes, whom they use for propaganda. The country’s investment in them — massive.

To show superiority, Putin, like Stalin, uses games to infiltrate subjects’ minds — as was utilized invading Hungary, the Balkans, Crimea, Afghanistan, now the Ukraine. Invasion through sport.

“Red Army” describes players paralleling the demise of the old USSR union. When totalitarianism broke apart, Russia’s hockey team followed the system. Anxieties of a nation were mirrored in its players. Fallen stars, once national heroes, became political enemies. When its great player Viacheslav Fetisov began losing, he was arrested by the KGB and beaten.

Subsequently named minister of sport, Fetisov — who’s since played hockey with Putin — helped bring the Olympics to Sochi. In Sochi, Putin threw Kremlin might in the world’s face. When his team lost, his face froze like the Steppes.

Stalin demonstrated superiority by producing top athletes. It hasn’t changed. Director Gabe Polsky: “I made ‘Red Army’ to honor the Soviet struggle and celebrate the art emerging from such a charged time in history.”

Sony Pictures Classics is presenting this official selection at the Cannes Film Festival. Producers are Jerry Weintraub and Werner Herzog.

Kelly: ‘Man’s word is law’

Facing Cannes head winds is Nicole Kidman in “Grace of Monaco.” The royals resent her Serene Highness Princess Grace’s portrayal. So let me reprise my old chat with Grace Kelly:

“For a happy marriage, the man must head the household. My husband is the undisputed ruler of our house. His word is law. Despite occasional problems, I accept that. Of course, I try to lobby now and then.

“Marriage to a prince, a European head of state, is different. I’ve had to adapt to his way of doing things.

“One must get away to recharge the batteries. Breaks are needed for my husband and me to communicate. At home, we always communicate via secretary. When I do catch him it’s to say there’s such and such’s party we must attend. And then we sit across a table with many people. It’s difficult.”

So is the palace homey? Feet up on a coffee table? “We have our private apartment, which I’ve done over in a modern manner. And I try to teach my children American ways. I don’t give them as much pocket money as their friends. I was brought up frugally, so I hold back many of their gifts.”

And, like us commoners, can two Serene Highnesses ever have a nice juicy fight?

“Of course there are . . . naturally . . . family disputes.” And does she holler in French or English? A well-bred laugh, then: “We always . . . er . . . have our family disputes in English.”

Pay attention

Kiddies, let mother tell you that despite smiles, jokes, voluntary retirement and quickly announced replacement, Letterman is very not happy — not — about giving it up . . . The Carlyle informed Mare Winningham soft fuzzy slippers await her after the June 8 Tonys . . . Italian foodie aficionado Bill Murray fed his cravings at Da Tommaso.

So, now, Starbucks wraps each Styrofoam container in: “Seek to be whole, not perfect” — Oprah Winfrey . . . “Blossom into more of who you really are” — Oprah Winfrey . . . “Every experience has meaning” — Oprah Winfrey . . . She offers tea drinkers “your own personal steep time.” Oy. Any local just craving a plain skim milk/Splenda/decaf/cinnamon/no whipped cream latte — try Dunkin’ Donuts.

Only in New York, kids, only in New York.