https://community.topcoder.com/stat?c=problem_statement&pm=13642

tc_ab.py

def swap(S, i1, i2):
	l = list(S)
	l[i1], l[i2] = l[i2], l[i1]
	S = ''.join(l)
	return S

def prependBs(S, N):
    nBs = N - len(S)
    return "B"*nBs + S

def createString(N, K):
    S = ""
    lA = 0
    rB = 0

    if K == 0:
        return prependBs(S, N)
    elif K == 1 and N >= 2:
        S = "AB"
        return prependBs(S, N)
    else:
        # the upper limit of pairs will be the approx roots of K
        lA = int(K**(1/2))
        rB = lA + 1
        if lA * rB < K:
            lA += 1
        
        # e.g. "AAABBB"
        curN = lA + rB
        curK = lA * rB
       
        # minimum possible value of N is lA + rB
        if curN > N:
            return S
        S = "A"*lA + "B"*rB
        
        # now we can adjust the string to have pairs in the  
        # range [lA + 1, lA * rB]
        if K < curK:
            swappos = curK - K
            S = swap(S, lA-1, lA-1+swappos)
            
        # prepend Bs (which doesn't add any pairs) if required
        if curN < N:
        	S = prependBs(S, N)

    return S
    
    
createString(10, 11)