You will need a better psu. Even if your 350watter is a name brand high quality unit I doubt it will work. The biggest power used in your system will be the video card, and it really does sip power: NV states that it maxes at 120Watts but there minimum system requirement is 400 watts with a minimum of 20amps continuous power on the 12V rail, and at least 1x6 pin PCI-E power connection.
Look at the side label of your psu and post the information on that label, including make model etc., or take a picture of the label and post; but at first glance I don't think you should try it.
Couple other reasons not to try it:
If it runs the new system, and you are into gaming etc., then there is a good chance the PSU will be running Hot and at nearly full output most of the time: This probably will lead to eventual failure and when it goes blewwy! it may kill other expensive components that you just bought.
2ndly: You didn't indicate what case or airflow you have nor if you plan to OC that "K" model CPU-but the PSU won't have any headroom for OCing nor will everything do well without adequate air flow.
Here's a reputable and adequate PSU for that build (if you can;t order from Newegg you can research this on www.pcpartpicker.com
SeaSonic S12G-450 450W ATX12V / EPS12V 80 PLUS GOLD Certified Active PFC Power Supply, Intel Haswell Ready
+ 10% off w/ promo code SSMAY10, ends 5/17
http://www.newegg.com/Product/Product.aspx?Item=N82E16817151139
XFX TS Series P1550SXXB9 550W ATX12V 2.2 & ESP12V 2.91 SLI Ready CrossFire Ready 80 PLUS Bronze Certified Active PFC Power Supply
http://www.newegg.com/Product/Product.aspx?Item=N82E16817207013