A321 Captain reported the number 2 engine failed due to bird strikes during initial climb. After handling the initial action items the flight crew followed special handling to a safe landing.

Narrative

ZZZ planned takeoff Runway XX. Winds were gusty; but straight down the runway. Performance was FLEX; config 3 with a takeoff weight around 172;500 pounds. Due to the gusty conditions; and busy airspace; I had briefed CONF 3 (flap overspeed) as a threat on departure. My plan to mitigate that threat was to engage the autopilot early. Due to aircraft weight; ZZZ1 was briefed as the landing airport if an issue causing a return to field were to arise.Takeoff and rotation were normal. Departure instructions per PDC was to fly heading 350. Around 350'; I engaged the autopilot; Captain selected heading close to the same moment. Passing 400' the airplane began to enter a right bank to fly the departure heading. At that instant we saw birds flash as they were illuminated by the aircraft lights. I heard thumps. I immediately looked at engine indications. I see #2 EPR (Engine Pressure Ratio) rolling back then turn amber. 'Engine failure my aircraft'. Captain [requested priority handling]. We were assigned present heading and 2000' by ATC. Flaps were retracted on schedule. I did the '3 pulls' to configure the airplane for a single engine climb. We noticed speed rapidly increasing; and that is when we realized after looking at N1 that the #2 engine was still producing thrust. Engine vibrations and engine noise at this point were excessive. ATC had leveled us at 2;000; and this was the moment I accepted a climb to 5;000. Meanwhile; the Captain was troubleshooting the issue. The Captain; per the ECAM placed the engines into the N1 mode; and we reduced #2 engine thrust to IDLE. At IDLE; engine vibrations were within acceptable parameters. The Captain set up the MCDU (Multifunction Control and Display Unit) for a landing at ZZZ1 Runway XYL. I briefed the approach and the Captain accomplished the descent checklist; and advised ATC we were ready for the approach. We flew the approach with #2 engine at IDLE. After landing the parking brake was set; #2 was shut down; and the Captain made a reassuring PA to the passengers as the ARFF (Airport Rescue and Firefighting) equipment assessed the damage. The safety equipment followed us to Gate X in ZZZ1.Cause: Continued advancements and investments towards improving wildlife awareness and mitigation technology.