ACR SMT CROSSED ACTIVE RWY WITHOUT CLRNC.

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AT APPROX XA17AM I WAS INSTRUCTED TO TAXI TO RWY 35 BY THE GND. I PROCEEDED TO TAXI TO RWY 32L. I THOUGHT THAT THE CTLR SAID 32L. I PROCEEDED TO TAXI TO RWY 32L AND CROSSED RWY 35; AND THAT IS WHEN THE CTLR CALLED ME AND TOLD ME THAT I HAD CROSSED AN ACTIVE RWY. I THEN TOLD HIM THAT I THOUGHT HE SAID TAXI TO RWY 32L. THE CTLR THEN SAID FOR ME TO HOLD SHORT OF RWY 32L AND CONTACT THE TWR. WE THEN CONTACTED THE TWR AND DEPARTED RWY 32L BOUND FOR MCI. I BELIEVE THE PROB WAS CAUSED BY FATIGUE AND A LACK OF COM BTWN MYSELF; THE TWR AND MY F/O. I BELIEVE THE PROB COULD BE SOLVED IF I WOULD HAVE BEEN MORE ALERT TO GND CTLRS INSTRUCTIONS; AND IF THE GND CTLR WOULD HAVE BEEN MORE OBSERVANT OF THE TFC FLOW ON THE ARPT. I BELIEVE AT THE TIME OF OCCURRENCE THE CTLR WAS HANDLING THE GND AND CLRNC DELIVERY. I HAD STOPPED PRIOR TO THE INTXN OF RWY 35 TO LOOK FOR TFC. IF THE CTLR HAD SEEN THIS IT WOULD HAVE BEEN PREVENTED. ALSO; MY F/O SHOULD HAVE ADVISED ME THAT I WAS TAXIING TO THE WRONG RWY. AT NO TIME WAS THERE ANY TFC CONFLICT. SUPPLEMENTAL INFO FROM ACN 93533: I CALLED UP OMA GND CTL TO GET TAXI CLRNC. THEY GAVE US CLRNC TO TAXI TO RWY 35. I READ BACK THE CLRNC TO TAXI TO RWY 35. THEN I SAID OUT LOUD TO THE CAPT; '35;' AND HE NODDED HIS HEAD.