It's a global day to celebrate women, but many fleeing Ukraine feel only the stress of finding a new life for their children as husbands, brothers and fathers stay behind to defend their country from Russia's invasion.

The number of refugees fleeing Ukraine reached 2 million on Tuesday, according to the United Nations, the fastest exodus Europe has seen since World War II.

Polina Shulga tried to ease the journey for her 3-year-old daughter by hiding the truth.

"Of course it's hard to travel with a child, but I explained to her that we're going on vacation and that we'll definitely come home one day when the war is over," Shulga said.

She didn't know what would come next after arriving in Hungary from Ukraine's capital, Kyiv, but believed the experience was making her stronger. "I feel like I'm responsible for my child, so it was easier for me to take this step and leave, because if I had not had a child, I probably would not have dared to go into the unknown," she said, as her little girl tugged at the hem of her coat.

Nataliya Grigoriyovna Levchinka, a refugee from Donetsk in eastern Ukraine, felt much the same.

"I'm generally in some kind of a terrible dream which keeps going on," the retired teacher said. "I would be in some kind of abstraction if it wasn't for my daughter. I wouldn't be able to come to my senses."

A decree by Ukraine's government that prohibits men aged 18 to 60 from leaving the country means that most of those fleeing Ukraine are women and children. The policy is meant to encourage men to sign up to fight against Russia's invasion or to keep them available for conscription into the armed forces.

That has led to heartbreaking scenes of separation, and growing worry as some encircled, battered parts of Ukraine slip out of reach.

In a refugee camp in Moldova, Elena Shapoval apologized for her tears. She doesn't hide them from her two children, one 4 and one 8, while recalling their journey from Odesa. The younger one doesn't understand what's happening, Shapoval said. The older one tries to calm her, saying, 'Mom, everything will be all right.'"

She cannot collapse as she thinks about the life they left behind. "I realize that we'll have to work a lot now," she said. "I need to get myself together because I have two children and I need to ball up my will like a fist."

In Romania, Alina Rudakova began to cry as the realized she had forgotten about International Women's Day. Last year, the 19-year-old from Melitopol received a bouquet of flowers from her father and gifts from other relatives.

"This year, I didn't even think about this day," she said. "This day was really awful."

In a theater at the Ukrainian Cultural Center in the Polish city of Przemysl near the border, women and children filled makeshift beds. Some checked their phones yet again for news.

"It was difficult to prepare myself for traveling," said one refugee from near Kyiv who gave only her first name, Natalia. "My sister said that I am very brave, but in my opinion I am a coward. I want to go home."

And at the Medyka border crossing in Poland, Yelena Makarova said her hurried flight from Kremenchuk with her mother and teenage daughter marked the end of her life as she knew it. Her father, husband and brother all stayed behind.

"I wish that (the war) it would finish as soon as possible, because do you know, for every mother, what can be worse?" she said. "I can't understand why our children are dying. I don't know."

From The Associated Press