Monthly Report with time-dependent navigational attribute

Hi,
We've a characteristic costcenter that has a navigational attribute called segment which is time-dependent attribute.
CostCenter-Segment master data is as follows.
COSTCENTER Segment          validFrom Valid To
============================================
CSTCNTER_1 SGMNT_A       10000101   20100831
CSTCNTER_1 SGMNT_B       20100901   99991231
Cube data is as follows. We don't have Segment in the cube. Also, no plans of adding segment to the cube.
COSTCENTER MONTH AMOUNT
========================
CSTCNTER_1 201007 100
CSTCNTER_1 201008 200
CSTCNTER_1 201009 300
CSTCNTER_1 201010 400
I'm trying to achieve monthly report by costcenter & segment as follows. Is there a way to achieve this?
COSTCENTER Segment MONTH AMOUNT
===============================
CSTCNTER_1 SGMNT_A 201007 100          (last day of 201007 is 20100731. as of 20100731, CSTCNTER_1 belongs to SGMNT_A)
CSTCNTER_1 SGMNT_A 201008 200          (last day of 201008 is 20100831. as of 20100831, CSTCNTER_1 belongs to SGMNT_A)
CSTCNTER_1 SGMNT_B 201009 300          (last day of 201009 is 20100930. as of 20100930, CSTCNTER_1 belongs to SGMNT_B)
CSTCNTER_1 SGMNT_B 201010 400          (last day of 201010 is 20101031. as of 20101031, CSTCNTER_1 belongs to SGMNT_B)
Appreciate any help.
-hari

thanks for looking into this.
I"ve already turned on SEGMENT as a navigational attribue in cube, for the reason, my current report looks like this.
COSTCENTER Segment MONTH AMOUNT
===============================
CSTCNTER_1 SGMNT_A 201007 100
CSTCNTER_1 SGMNT_A 201008 200
CSTCNTER_1 SGMNT_A 201009 300 I'm expecting this should show up in SGMNT_B
CSTCNTER_1 SGMNT_A 201010 400 I'm expecting this should show up in SGMNT_B
But, I'm expecting the report look like this
COSTCENTER Segment MONTH AMOUNT
===============================
CSTCNTER_1 SGMNT_A 201007 100
CSTCNTER_1 SGMNT_A 201008 200
CSTCNTER_1 SGMNT_B 201009 300
CSTCNTER_1 SGMNT_B 201010 400

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